# Desmos graphing

Desmos graphing β Example Problem Problem: For the given equation, a. Identify the y-intercept(s) and the x-intercept(s) if they exist. Show your work. b. Following example 1.2.3 in the eText, calculate the coordinates of 8 points on the graph (these can include the intercepts). c. Using Desmos, plot the points on the graph (SEE THE EXAMPLE PROBLEM). Be sure to label the xand y-axes! Add the graph of the equation and scale appropriately. d. Test for symmetry about each axis and the origin. Explain your reasoning. Equation: π¦ = π₯ 3 β8 4 a. y-intercept: (0, β2) π¦= 0β8 4 8 π¦=β 4 π¦ = β2 b. Determine coordinates of points on this line: π₯ β3 π¦ β 35 4 π₯3 β 8 = 0 (β2, β4) β1 β 9 4 9 (β1, β ) 4 0 β2 (0, β2) 1 β 7 4 7 (1, β ) 4 2 0 3 19 4 (3, 4 14 (4, 14) 3 π₯ = β8 π₯=2 35 ) 4 β4 3 π₯ =8 (β3, β β2 x-intercept: (2, 0) π₯3 β 8 0= 4 (π₯, π¦) (2, 0) 19 ) 4 c. To create a graph of this equation, go to https://www.desmos.com/calculator i. Create a table by clicking the βAdd Itemβ button and selecting βtableβ. ii. An empty table will appear, and it will expand downward as you fill it in. iii. Enter the values from your table, and a graph of these points will appear at the right. iv. Now enter the equation to draw the graph of the equation containing these points. v. Click on the Graph Settings icon (wrench at upper right corner). Add axis labels where shown. Then scale the graph so that all the points are visible and the main features of the graph can be seen (such as curves and inflection points). For this graph, the scale β10 β€ π₯ β€ 10 and β15 β€ π¦ β€ 20 is appropriate. vi. Once your graph is complete, you are ready to export it. Click on the βShare Graphβ icon at the top of the screen, then click on βExport Imageβ. vii. Make sure your graph looks correct and the axis labels are visible. Click βDownload PNGβ and save your file to your computer. Include the problem number in the name of your file. d. To test for symmetry about each axis, determine whether the graph can be reflected about the axis without changing the resulting graph. Symmetry about the x-axis requires each point (a, b) and (a, -b) to be on the graph, and symmetry about the y-axis requires (a, b), and (-a, b) to exist. Symmetry about the origin is present if for each point (a, b) corresponds to a point (-a, -b) on the graph. Test for symmetry algebraically, then show an example from your graph. For the equation π¦ = π₯ 3 β8 4 i. Symmetry about the x-axis: No. To test, substitute (π₯, βπ¦) for (π₯, π¦) in the equation and solve for y. Do you get the same equation? βπ¦ = π₯3 β 8 4 βπ₯ 3 + 8 π¦= 4 For example, the point (-2, -4) is on the graph but (-2, 4) is not. ii. Symmetry about the y-axis: No. To test, substitute (βπ₯, π¦) for (π₯, π¦) in the equation and solve for y. π¦= (βπ₯)3 β 8 4 π¦= βπ₯ 3 β 8 4 For example, the point (-2, -4) is on the graph but (2, -4) is not. iii. Symmetry about the origin: No. To test, substitute (βπ₯, βπ¦) for (π₯, π¦) in the equation and solve for y. βπ¦ = π¦= (βπ₯)3 β 8 4 π₯3 + 8 4 For example, the point (-2, -4) is on the graph but (2, 4) is not. umuc login Log In UMG X | Desmos Grapx Discussion_W X (Desmos grap Desmos | Gra X studypool log x S SOLUTION: M X + Π₯ o a O https://learn.umgc.edu/content/enforced/643441-005890-01-2215-OL2-6988/Discussion_W2.pdf?_8d21SessionVal=1W8Y3KNKZhuGA… of TI η Set Microsoft Edge as the default application for reading PDF files? Set as default 1 of 2 a – + Q (L Page view A Read aloud V Draw Highlight Erase a A Week 2 Discussion Problems For the given equation, a. Identify the y-intercept(s) and the x-intercept(s) if they exist. Show your work. b. Following example 1.2.3 in the eText, calculate the coordinates of 8 points on the graph (these can include the intercepts). C. Using Desmos, plot the points on the graph (SEE THE EXAMPLE PROBLEM). Be sure to label the x- and y-axes! Add the graph of the equation and scale appropriately. d. Test for symmetry about each axis and the origin. Explain your reasoning. 01. 3x + 2y = 9 02. y = 2Vx+1-5 03. y2 = 2x 04 y = x – 1 05. x2 + y – 4)2 = 16 06. x2 – (2y)2 = 9 07. y = -2×2 + 1 08. y = x2 β 3x – 4 09. y = x3 – 4x For the given equation, a. Determine algebraically whether the equation represents y as a function of x. Explain your reasoning. Type here to search 71Β°F Partly sunny Oo )) 6:36 PM 6/25/2021 10 719

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