DETAILED ACTION
This action is responsive to the Amendments and Remarks received 06/18/2026 and 07/10/2026 in which claims 2 and 11 are cancelled, claims 1, 4, 5, 7, 10, 13, 14, 16, and 19 are amended, and claim 20 is added as a new claim.
Response to Arguments
On page 11 of the Remarks (06/18/2026), Applicant contends the combination of cited references fails to disclose, teach, or suggest “the control performed in response to accepting a first selection operation with respect to one of a plurality of graphs shown on a selection screen with coordinate axes.” Examiner disagrees. As explained in the rejections, infra, the cited references teach graphing calculators able to plot a plurality of graphs simultaneously on the same coordinate plane and capable of presenting a menu to a user that allows the user to select from a number of functions that can provide information such as min/max, x- or y-intercept, intersection, etc. Anyone with any experience using a graphing calculator would understand the features recited in the claims anticipated or obvious in view of the cited references. Applicant’s arguments do not particularly explain why the cited teachings of TI fail to disclose a menu for selecting a graphed mathematical function or why the teachings of TI fail to disclose a menu for selecting an analysis tool. For example, why doesn’t TI’s page 218, teaching an “Analyze Graph” menu and the “Minimum” function within that menu, teach the averred feature? Because Applicant does not particularly address the rejection of record, Applicant’s Remarks are unpersuasive of error.
On page 11 of the Remarks (06/18/2026), Applicant contends the combination of cited references fails to disclose, teach, or suggest “the control performed in response to confirmation of the selected graph on the selection screen” including displaying the graphs with the same color density. As explained in the rejections, infra, Examiner found that manipulating color density according to the type of graph analysis function selected was disclosed, taught, or suggested by the cited prior art. TI discloses the ability to select and de-select certain graphs displayed concurrently and the ability to select which data to include on the display. TI further discloses that information regarding a graph analysis function can be included in the display of the selected graph and that such a display can indicate the selected graph through color density adjustment when the graph analysis tool implicated is of a type that would only apply to one of the plurality of displayed graphs. Such a teaching, to one of ordinary skill, equally teaches the converse, which is that when the graph analysis function is “intersection” or perhaps “trace all,” such a graph analysis tool type corresponds with no particular graphed mathematical function such that no color density adjustment would be desirable. Therefore, as demonstrated in the rejections, infra, TI discloses the claimed feature. In addition, for the alternative rejection under 35 U.S.C. 103, the combination of Education and Frisch teaches changing color density of graphed mathematical functions depending on selection of appropriate graph analysis tools and Examiner finds the skilled artisan would understand that where the function is applicable to both graphed functions simultaneously, it would be undesirable to visually depict that only one of the graphs is selected. See rationale of rejections, explained in further detail, infra. For all the foregoing reasons, Examiner is not persuaded of error or patentability.
Other claims are not argued separately. Remarks (06/18/2026), 11–12.
Claim Rejections - 35 USC § 102
The following is a quotation of the appropriate paragraphs of 35 U.S.C. 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale or otherwise available to the public before the effective filing date of the claimed invention.
(a)(2) the claimed invention was described in a patent issued under section 151, or in an application for patent published or deemed published under section 122(b), in which the patent or application, as the case may be, names another inventor and was effectively filed before the effective filing date of the claimed invention.
Claims 1, 3–10, and 12–20 are rejected under 35 U.S.C. 102(a)(1) as being anticipated by “TI-Nspire CX Premium Teacher Software Guidebook,” Texas Instruments Incorporated, 2006-2019. pp. 1-621 (herein “TI”).
Regarding claim 1, TI discloses an electronic device comprising: a display; and at least one processor, wherein the at least one processor: shows, on the display, a selection screen for accepting a first selection operation the selection screen including plurality of graphs shown on the display with coordinate axes, and each of the plurality of graphs including first information; in response to accepting the first selection operation with respect to one of the plurality of graphs: sets the one of the plurality of graphs as a selected graph the first information of which is to be shown; sets one or more remaining graphs other than the selected graph among the plurality of graphs as an unselected graph the first information of which is not to be shown (TI, page 242: disclosing that currently hidden items are shown dimmed, which also means unhidden items would be not dimmed; see also TI, pages 211–212: discloses the ability to hide and show individual graphs wherein if multiple graphs are shown they would normally be displayed using the same color density so as to not indicate that a particular graph was selected as disclosed on TI, pages 217–219, discloses any other information related to the graphed functions can similarly be shown or hidden, and discloses a checkbox for selecting which functions will be displayed allowing multiple simultaneous graphs to be either included or excluded from being displayed and shows the graphs being displayed with the coordinate axes; see also top figure at TI, page 236; see also TI, page 247: disclosing trace all which does not select a particular graph); and displays the unselected graph with a lower color density than a color density of the selected graph (see supra and infra); and in response to the selected graph being confirmed on the selection screen, shows, on the display a first information display screen on which the first information relating to the selected graph is shown along with the coordinate axes and the plurality of graphs (see supra and infra), wherein the plurality of graphs are displayed with a same color density on the first information display screen (Examiner interprets this limitation consistent with paragraph [0066] of Applicant’s published Specification wherein it is explained that Applicant’s Figs. 8 and 9 show two functions graphed on the same screen and a first function can be selected and shown in a dark black wherein a second function can be shown in a lighter gray and the selected function can have a further analysis performed thereon, like y-intercept, Min/Max, or listing of the function’s mathematical expression, etc. but the non-selected function/graph does not have further information displayed thereabout; TI, pages 217–219: describe a graphing calculator capable of plotting two functions simultaneously wherein the user can select which function to further analyze and display information thereabout, for example the minimum of the first graph and displaying first information about the selected graph but not second information about the non-selected graph; TI, pages 211–212: discloses the ability to hide and show individual graphs or any other information related to the graphed functions and discloses a checkbox for selecting which functions will be displayed allowing multiple simultaneous graphs to be either included or excluded from being displayed and shows the graphs being displayed with the coordinate axes; Consistent with Applicant’s paragraph [0066] of Applicant’s published Specification, the color density can be a level of gray; TI, pages 217–219: describe a graphing calculator capable of plotting two functions simultaneously wherein the user can select which function to further analyze wherein the selected graph is displayed in a darker gray level (i.e. dark gray or black) and the non-selected graph is displayed in a lighter gray level; see also TI, page 242: disclosing that currently hidden items are shown dimmed; The skilled artisan would understand equal graphic weighting (e.g. no highlighting/emphasis) is beneficial when it would not make sense to select a single graph, such as when the graphing calculator is displaying information about where the graphs intersect one another; An “intersection” function does not apply to a single graphed mathematical function, but is instead a shared characteristic among the graphed functions being displayed; Examiner further finds that, as an appearance behavior, aesthetic elements, per se, are not properly the subject of utility patents and are ornamental unless tied to a functional improvement of the computing device).
Regarding claim 3, TI discloses the electronic device according to claim 1, wherein the first information is any one of: i) a coordinate value of an intercept of the selected graph and one of the coordinate axes orthogonal to each other; ii) a maximum value or a minimum value in a predetermined range of the selected graph; and iii) a coordinate value with respect to one of the two coordinate axes corresponding to a predetermined coordinate value with respect to the other one of the two coordinate axes (TI, pages 217–219: describe a graphing calculator capable of plotting two functions simultaneously wherein the user can select which function to further analyze and display information thereabout, for example the minimum using lower and upper bounds to set the range; other tools like max, y-intercept, etc. work similarly; see also TI, page 246–247: discloses trace and trace all which provide, for points on the graph, displayed coordinate values).
Regarding claim 4, TI discloses the electronic device according to claim 1, wherein the at least one processor: accepts, when showing on the display a second information display screen on which is shown second information that is different from the first information and that relates to one of the plurality of graphs, a second selection operation for selecting a graph the second information of which is to be shown among the plurality of graphs while showing the second information display screen (TI, pages 211–212: discloses the ability to hide and show individual graphs or any other information related to the graphed functions and discloses a checkbox for selecting which functions will be displayed allowing multiple simultaneous graphs to be either included or excluded from being displayed and shows the graphs being displayed with the coordinate axes); and displays the plurality of graphs with a same color density while showing the second information display screen (TI, page 242: disclosing that currently hidden items are shown dimmed, which also means unhidden items would be not dimmed; see also TI, pages 211–212: discloses the ability to hide and show individual graphs wherein if multiple graphs are shown they would normally be displayed using the same color density so as to not indicate that a particular graph was selected as disclosed on TI, pages 217–219, discloses any other information related to the graphed functions can similarly be shown or hidden, and discloses a checkbox for selecting which functions will be displayed allowing multiple simultaneous graphs to be either included or excluded from being displayed and shows the graphs being displayed with the coordinate axes; see also top figure at TI, page 236; see also TI, page 247: disclosing trace all which does not select a particular graph).
Regarding claim 5, TI discloses the electronic device according to claim 4, wherein a maximum amount of time required for performing processing to calculate the first information by the at least one processor is longer than a maximum amount of time required for performing processing to calculate the second information by the at least one processor (Examiner notes this wherein clause appears to contain no patentable feature and merely explains a happenstance that is controllable by mathematical complexity and user selection; Examiner finds the processing time is proportional to the complexity of the equation; TI, page 246: illustrates a linear function and an exponential function wherein the exponential function would take longer to process).
Regarding claim 6, TI discloses the electronic device according to claim 4, wherein the second information is information on a coordinate value of a trace position on the graph when the graph is traced or information on a tangent line at a predetermined position on the graph (TI, page 253: discloses creating a tangent line at any point on the graph; TI, page 246–247: discloses trace and trace all which provide, for points on the graph, displayed coordinate values).
Regarding claim 7, TI discloses the electronic device according to claim 1, wherein the at least one processor is configured to display the plurality of graphs in line styles different from each other (TI, page 249: discloses in the figure different line styles being used for different graphed objects).
Regarding claim 8, TI discloses the electronic device according to claim 1, wherein the at least one processor applies a display style of the selected graph to an intersection of the selected graph and the unselected graph on the selection screen (TI, page 252: illustrates two graphs with intersection wherein the selected shape (the triangle) covers the intersection region of the circle; Examiner finds the skilled artisan can imagine the opposite configuration wherein the intersecting region covering the triangle would be shaded with the darker gray of the circle if the circle were the selected function rather than the triangle).
Regarding claim 9, TI discloses the electronic device according to claim 1, wherein the at least one processor displays, on the selection screen, the selected graph with a color density same as the color density with which the plurality of graphs are displayed on the first information display screen (TI, page 242: disclosing that currently hidden items are shown dimmed, which also means unhidden items would be not dimmed; see also TI, pages 211–212: discloses the ability to hide and show individual graphs wherein if multiple graphs are shown they would normally be displayed using the same color density so as to not indicate that a particular graph was selected as disclosed on TI, pages 217–219, discloses any other information related to the graphed functions can similarly be shown or hidden, and discloses a checkbox for selecting which functions will be displayed allowing multiple simultaneous graphs to be either included or excluded from being displayed and shows the graphs being displayed with the coordinate axes; see also top figure at TI, page 236; see also TI, page 247: disclosing trace all which does not select a particular graph).
Claim 10 lists the same elements as claim 1, but in method form rather than system form. Therefore, the rationale for the rejection of claim 1 applies to the instant claim.
Claim 12 lists the same elements as claim 3, but in method form rather than system form. Therefore, the rationale for the rejection of claim 3 applies to the instant claim.
Claim 13 lists the same elements as claim 4, but in method form rather than system form. Therefore, the rationale for the rejection of claim 4 applies to the instant claim.
Claim 14 lists the same elements as claim 5, but in method form rather than system form. Therefore, the rationale for the rejection of claim 5 applies to the instant claim.
Claim 15 lists the same elements as claim 6, but in method form rather than system form. Therefore, the rationale for the rejection of claim 6 applies to the instant claim.
Claim 16 lists the same elements as claim 7, but in method form rather than system form. Therefore, the rationale for the rejection of claim 7 applies to the instant claim.
Claim 17 lists the same elements as claim 8, but in method form rather than system form. Therefore, the rationale for the rejection of claim 8 applies to the instant claim.
Claim 18 lists the same elements as claim 9, but in method form rather than system form. Therefore, the rationale for the rejection of claim 9 applies to the instant claim.
Claim 19 lists the same elements as claim 1, but in CRM form rather than system form. Therefore, the rationale for the rejection of claim 1 applies to the instant claim.
Regarding claim 20, TI discloses the electronic device according to claim 1, wherein, in response to accepting a second selection operation for showing information common to the plurality of graphs, the at least one processor displays the first information display screen without displaying the selection screen (TI, page 242: disclosing that currently hidden items are shown dimmed, which also means unhidden items would be not dimmed; see also TI, pages 211–212: discloses the ability to hide and show individual graphs wherein if multiple graphs are shown they would normally be displayed using the same color density so as to not indicate that a particular graph was selected as disclosed on TI, pages 217–219, discloses any other information related to the graphed functions can similarly be shown or hidden, and discloses a checkbox for selecting which functions will be displayed allowing multiple simultaneous graphs to be either included or excluded from being displayed and shows the graphs being displayed with the coordinate axes; see also top figure at TI, page 236; see also TI, page 247: disclosing trace all which does not select a particular graph; Examiner finds the skilled artisan would interpret TI to be disclosing that when information pertains to both graphs, for example the intersection function, it would not make sense to demonstrate a particular graph was chosen using highlighting since intercept applies to both graphed functions simultaneously; The skilled artisan would understand equal graphic weighting (e.g. no highlighting/emphasis) is beneficial when it would not make sense to select a single graph, such as when the graphing calculator is displaying information about where the graphs intersect one another; An “intersection” function does not apply to a single graphed mathematical function, but is instead a shared characteristic among the graphed functions being displayed; Examiner further finds that, as an appearance behavior, aesthetic elements, per se, are not properly the subject of utility patents and are ornamental unless tied to a functional improvement of the computing device).
Claim Rejections - 35 USC § 103 (alternative grounds)
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102 of this title, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1, 3, 4, 6–10, 12, 13, and 15–20 are rejected under 35 U.S.C. 103 as being unpatentable over Texas Instruments Education, “How to Graph on the TI-84 Plus CE,” accessed at https://www.youtube.com/watch?v=BPfRVa-PB7Y on 03/13/2026, July 14, 2023 (herein “Education”) and Kayt Frisch, “Plot in Grayscale using Matlab,” accessed at https://www.youtube.com/watch?v=O4IPR8eoMs4 on 03/13/2026, Sept. 24, 2020 (herein “Frisch”).
Regarding claim 1, the combination of Education and Frisch teaches or suggests an electronic device comprising: a display; and at least one processor, wherein the at least one processor: shows, on the display, a selection screen for accepting a first selection operation the selection screen including plurality of graphs shown on the display with coordinate axes, and each of the plurality of graphs including first information; in response to accepting the first selection operation with respect to one of the plurality of graphs: sets the one of the plurality of graphs as a selected graph the first information of which is to be shown; sets one or more remaining graphs other than the selected graph among the plurality of graphs as an unselected graph the first information of which is not to be shown (see infra); shows on the display a first information display screen on which the first information relating to the selected graph is shown with the coordinate axes and the plurality of graphs when the selected graph is confirmed on the selection screen (Examiner interprets this limitation consistent with paragraph [0066] of Applicant’s published Specification wherein it is explained that Applicant’s Figs. 8 and 9 show two functions graphed on the same screen and a first function can be selected and shown in a dark black wherein a second function can be shown in a lighter gray and the selected function can have a further analysis performed thereon, such as min, max, y-intercept, or listing of the function’s mathematical expression, etc. but the non-selected function does not have further information displayed thereabout; Education, Minute 1:42: teaches two functions graphed and then calculating min, max, coordinates, x- and y-intercepts, and intersection points and wherein those coordinate values are displayed based on which graph is selected and only those values corresponding to the selected graph are displayed); and displays the unselected graph with a lower color density than a color density of the selected graph (see supra and infra); and in response to the selected graph being confirmed on the selection screen, shows, on the display a first information display screen on which the first information relating to the selected graph is shown along with the coordinate axes and the plurality of graphs (see supra and infra), wherein the plurality of graphs are displayed with a same color density on the first information display screen (While Education teaches color values differentiating one graphed function from another, Frisch teaches utilizing gray scale values to distinguish between graphed functions for purposes of color blindness or generating graphs for publication in black and white; Frisch teaches adding an alpha parameter to the color value for plotting graphs in grayscale which is important for publishing in non-color reproductions and for those who are color blind. It also teaches line style like line thickness can be changed; see also Education, Minute 5:20: teaches the same color density for both graphed functions; The skilled artisan would understand equal graphic weighting (e.g. no highlighting/emphasis) is beneficial when it would not make sense to select a single graph, such as when the graphing calculator is displaying information about where the graphs intersect one another; An “intersection” function does not apply to a single graphed mathematical function, but is instead a shared characteristic among the graphed functions being displayed; Examiner further finds that, as an appearance behavior, aesthetic elements, per se, are not properly the subject of utility patents and are ornamental unless tied to a functional improvement of the computing device).
One of ordinary skill in the art, before the effective filing date of the claimed invention, would have been motivated to combine the elements taught by Education, with those of Frisch, because both references are drawn to the same field of endeavor such that one wishing to practice graphing mathematical functions using a computing device and display would be led to their relevant teachings and because, as Frisch explains, one skilled in the art would be led to use grayscale rather than Education’s color differentiation to differentiate between graphed functions for purposes of generating graphics that can be used in publications that may not necessarily be reproduced in color and because it is more accessible for color blind users. Therefore, the combination is a mere combination of prior art elements, according to known methods, to yield a predictable result. This rationale applies to all combinations of Education and Frisch used in this Office Action unless otherwise noted.
Regarding claim 3, the combination of Education and Frisch teaches or suggests the electronic device according to claim 1, wherein the first information is any one of: i) a coordinate value of an intercept of the selected graph and one of the coordinate axes orthogonal to each other; ii) a maximum value or a minimum value in a predetermined range of the selected graph; and iii) a coordinate value with respect to one of the two coordinate axes corresponding to a predetermined coordinate value with respect to the other one of the two coordinate axes (Education, Minute 1:41–4:43 et seq. teaches finding the min, max, intercepts, etc. and defining lower and upper bounds for finding these points wherein the coordinates are displayed upon their finding).
Regarding claim 4, the combination of Education and Frisch teaches or suggests the electronic device according to claim 1, wherein the at least one processor: accepts, when showing on the display a second information display screen on which is shown second information that is different from the first information and that relates to one of the plurality of graphs, a second selection operation for selecting a graph the second information of which is to be shown among the plurality of graphs while showing the second information display screen; and displays the plurality of graphs with a same color density while showing the second information display screen (Education, Minute 2:25–2:45: illustrates how one can analyze either graph by moving between them through selection and getting only the information corresponding to the selected function, such information including coordinates from tracing, minima, maxima, intercepts, etc.).
Regarding claim 6, the combination of Education and Frisch teaches or suggests the electronic device according to claim 4, wherein the second information is information on a coordinate value of a trace position on the graph when the graph is traced or information on a tangent line at a predetermined position on the graph (Education, Minute 1:25–2:45 and 3:02 et seq.: illustrates how one can analyze either graph by moving between them through selection and getting only the information corresponding to the selected function, such information including coordinates from tracing, minima, maxima, intercepts, etc.; Examiner notes the slope of a tangent line on a curve at a specific point is equal to the function’s derivative at that point; Education, Minute 4:42: teaches the derivative of a curve can be calculated using option 6 and then you could just trace the derivative curve to find the slope at the desired point and plot that linear curve).
Regarding claim 7, the combination of Education and Frisch teaches or suggests the electronic device according to claim 1, wherein the at least one processor is configured to display the plurality of graphs in line styles different from each other (Frisch, Minute 2:02–2:09: teaches using different line styles including different widths, dashes, dots, etc.).
Regarding claim 8, the combination of Education and Frisch teaches or suggests the electronic device according to claim 1, wherein the at least one processor applies a display style of the selected graph to an intersection of the selected graph and the unselected graph on the selection screen (Education, 4:48–5:25: teaches an intersection point being displayed between two graphs according to a style, the style parameters including a blinking box at the intersection point, the first graph being selected such that the intersection point’s coordinates are displayed with respect to the first graphed function (i.e. red)).
Regarding claim 9, the combination of Education and Frisch teaches or suggests the electronic device according to claim 1, wherein the at least one processor displays, on the selection screen, the selected graph with a color density same as the color density with which the plurality of graphs are displayed on the first information display screen (Examiner notes that where two graphs are displaying an intersection, the intersection applies equally to both graphs such that it does not make sense to display the two graphs in a way that indicates one graph or the other is selected; Education, 4:48–5:25: teaches an intersection point being displayed between two graphs of equal color density according to a style, the style parameters including a blinking box at the intersection point, the first graph being selected such that the intersection point’s coordinates are displayed with respect to the first graphed function (i.e. red); Again, Examiner notes the selected function could be the blue function in Education and the intersection point coordinates would be identical).
Claim 10 lists the same elements as claim 1, but in method form rather than system form. Therefore, the rationale for the rejection of claim 1 applies to the instant claim.
Claim 12 lists the same elements as claim 3, but in method form rather than system form. Therefore, the rationale for the rejection of claim 3 applies to the instant claim.
Claim 13 lists the same elements as claim 4, but in method form rather than system form. Therefore, the rationale for the rejection of claim 4 applies to the instant claim.
Claim 15 lists the same elements as claim 6, but in method form rather than system form. Therefore, the rationale for the rejection of claim 6 applies to the instant claim.
Claim 16 lists the same elements as claim 7, but in method form rather than system form. Therefore, the rationale for the rejection of claim 7 applies to the instant claim.
Claim 17 lists the same elements as claim 8, but in method form rather than system form. Therefore, the rationale for the rejection of claim 8 applies to the instant claim.
Claim 18 lists the same elements as claim 9, but in method form rather than system form. Therefore, the rationale for the rejection of claim 9 applies to the instant claim.
Claim 19 lists the same elements as claim 1, but in CRM form rather than system form. Therefore, the rationale for the rejection of claim 1 applies to the instant claim.
Regarding claim 20, the combination of Education and Frisch teaches or suggests the electronic device according to claim 1, wherein, in response to accepting a second selection operation for showing information common to the plurality of graphs, the at least one processor displays the first information display screen without displaying the selection screen (Examiner interprets this limitation consistent with paragraph [0066] or [0076] of Applicant’s published Specification wherein it is explained that Applicant’s Figs. 8 and 9 show two functions graphed on the same screen and a first function can be selected and shown in a dark black wherein a second function can be shown in a lighter gray and the selected function can have a further analysis performed thereon, such as min, max, y-intercept, or listing of the function’s mathematical expression, etc. but the non-selected function does not have further information displayed thereabout; Education, Minute 1:42: teaches two functions graphed and then calculating min, max, coordinates, x- and y-intercepts, and intersection points and wherein those coordinate values are displayed based on which graph is selected and only those values corresponding to the selected graph are displayed; While Education teaches color values differentiating one graphed function from another, Frisch teaches utilizing gray scale values to distinguish between graphed functions for purposes of color blindness or generating graphs for publication in black and white; Frisch teaches adding an alpha parameter to the color value for plotting graphs in grayscale which is important for publishing in non-color reproductions and for those who are color blind. It also teaches line style like line thickness can be changed; Education, Minute 5:20: teaches the same color density for both graphed functions; The skilled artisan would understand equal graphic weighting (e.g. no highlighting/emphasis) is beneficial when it would not make sense to select a single graph, such as when the graphing calculator is displaying information about where the graphs intersect one another; An “intersection” function does not apply to a single graphed mathematical function, but is instead a shared characteristic among the graphed functions being displayed; Examiner further finds that, as an appearance behavior, aesthetic elements, per se, are not properly the subject of utility patents and are ornamental unless tied to a functional improvement of the computing device).
Claims 5 and 14 are rejected under 35 U.S.C. 103 as being unpatentable over Education, Frisch, and Kisker Education Videos, “TI-84 Tutorial: Using the INTERSECT feature to solve for x,” accessed at https://www.youtube.com/watch?v=gp1xBaW8hlM on 03/13/2026, January 9, 2014 (herein “Kisker”)
Regarding claim 5, the combination of Education, Frisch, and Kisker teaches or suggests the electronic device according to claim 4, wherein a maximum amount of time required for performing processing to calculate the first information by the at least one processor is longer than a maximum amount of time required for performing processing to calculate the second information by the at least one processor (Kisker, Minute 2:09 and 2:45 shows a first function x^3+4x^2-8x taking much more time to graph than the second function equal to 96 wherein the functions are plotted together to perform an intersection analysis).
One of ordinary skill in the art, before the effective filing date of the claimed invention, would have been motivated to combine the elements taught by Education and Frisch, with those of Kisker, because all three references are drawn to the same field of endeavor such that one wishing to practice graphing mathematical functions using a computing device and display would be led to their relevant teachings and because, as Kisker demonstrates, one skilled in the art would understand that more complex mathematical functions take a graphing calculator longer to “draw” such that the combination is a mere combination of prior art elements, according to known methods, to yield a predictable result. This rationale applies to all combinations of Education, Frisch, and Kisker used in this Office Action unless otherwise noted.
Claim 14 lists the same elements as claim 5, but in method form rather than system form. Therefore, the rationale for the rejection of claim 5 applies to the instant claim.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Tutor Terrific, “Calculator Tutorial – TI-83 Plus Graphing Features,” accessed at https://www.youtube.com/watch?v=0We4zLBOV_o&list=PLWhk-wyswezeUBpOfbZKp8Ql93DzgmXOg&index=6 on 03/13/2026, January 18, 2019. This video shows multiple graphs on a monochrome display and includes features like value, zero, min, max, intersect, etc. (Minute 15:25). Minute 14:28–15:20 teaches you can change the line style of each function displayed on the display together. Minute 19:00 teaches the intersect points can be graphed using several styles or shape types such as squares, pluses, or dots and turning on and off plots (Minute 19:18).
Texas Instruments Education, “Modes, Settings and Organization on the TI-84 Plus CE,” accessed at https://www.youtube.com/watch?v=gcESDY1g1ls&list=PLQa_6aWmaC6A7NMb83r-jNi_5gyg6TE2R&index=4 on 03/13/2026, July 14, 2023. This video teaches some graph settings or modes for simultaneous graphs and line style such as Thick, Dot-Thick, Dot-Thin, etc. (Minute 6:20–7:00).
“TI-Nspire CX Premium Teacher Software Guidebook,” Texas Instruments Incorporated, 2006-2019. pp. 1-621. Pages 266 and 317 explain how line styles in graphs can be changed, e.g. from Thick, Thin, or medium to another style. Pages 318, 320, and 321 show that color density can be changed for graphs achieving different levels of grayscale based on whether the object is selected. Page 219 shows graphs in different levels of grayscale and the selected function darker than the non-selected function when functions are graphed simultaneously.
TI Australia, “Plot Graphs and Window Settings | TI-Nspire CX II CAS | Getting Started Series – Graphs Application,” accessed at https://www.youtube.com/watch?v=N_tRS-tI9nk, on 03/13/2026, September 13, 2021. Minute 5:45 teaches changes the line style for a graphed function to a dashed line, for example. Minute 6:05 teaches the colors can be levels of gray scale.
TI Australia, “Analysing Graphs | TI-Nspire CX II CAS | Getting Started Series – Graphs Application,” accessed at https://www.youtube.com/watch?v=bRl6NAnAqGU, on 03/13/2026, September 13, 2021. Minute 1:06 et seq. teaches finding the min, max, intercepts, etc. and defining lower and upper bounds for finding these points wherein the coordinates are displayed upon their finding.
TI Australia, “Analysing Graphs | TI-84 Plus CE | Getting Started Series – Graphing,” accessed at https://www.youtube.com/watch?v=djD5BnyX39c, on 03/13/2026, January 16, 2022.
Brothers (US 2020/0151136 A1) teaches handheld graphing calculators.
THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any extension fee pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to Michael J Hess whose telephone number is (571)270-7933. The examiner can normally be reached Mon - Fri 9:00am-5:30pm.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, William Vaughn can be reached on (571)272-3922. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8933.
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/MICHAEL J HESS/Examiner, Art Unit 2481
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