MATH 107 University of Maryland College Desmos Graphing Questions

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 caninclude 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. Practice for symmetry about each axis and the origin. Explain your reasoning.

𝑦 = √𝑥 − 1

Desmos graphing – 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: 𝑦 =
𝑥 3 −8
4
a. y-intercept: (0, −2)
𝑦=
0−8
4
8
𝑦=−
4
𝑦 = −2
b. Determine coordinates of
points on this line:
𝑥
−3
𝑦
−
35
4
𝑥3 − 8 = 0
(−2, −4)
−1
−
9
4
9
(−1, − )
4
0
−2
(0, −2)
1
−
7
4
7
(1, − )
4
2
0
3
19
4
(3,
4
14
(4, 14)
3
𝑥 = √8
𝑥=2
35
)
4
−4
3
𝑥 =8
(−3, −
−2
x-intercept: (2, 0)
𝑥3 − 8
0=
4
(𝑥, 𝑦)
(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 “Add Item”
button and selecting “table”.
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 −10 ≤ 𝑥 ≤ 10
and −15 ≤ 𝑦 ≤ 20 is appropriate.
vi. Once your graph is complete, you are ready to export it. Click on the “Share Graph” icon
at the top of the screen, then click on “Export Image”.
vii. Make sure your graph looks correct and the axis labels are visible. Click “Download PNG”
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 𝑦 =
𝑥 3 −8
4
i. Symmetry about the x-axis: No. To test, substitute (𝑥, −𝑦) for (𝑥, 𝑦) in the
equation and solve for y. Do you get the same equation?
−𝑦 =
𝑥3 − 8
4
−𝑥 3 + 8
𝑦=
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 (−𝑥, 𝑦) for (𝑥, 𝑦) in the
equation and solve for y.
𝑦=
(−𝑥)3 − 8
4
𝑦=
−𝑥 3 − 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 (−𝑥, −𝑦) for (𝑥, 𝑦) in the
equation and solve for y.
−𝑦 =
𝑦=
(−𝑥)3 − 8
4
𝑥3 + 8
4
For example, the point (-2, -4) is on the graph but (2, 4) is not.
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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 – 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.
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