Question 1

Which of the following is the correct procedure to find the x-intercept(s) of the graph of an equation?

Accepted Answer

Set $$y = 0 in $$the equation and solve for $$x.$$

Question 2

A graph is said to be symmetric with respect to the y-axis if, for every point $$(x, y) on $$the graph, which of the following points is also on the graph?

Accepted Answer

$$(-x, y)$$

Question 3

To test an equation for symmetry with respect to the origin, what substitutions should you make?

Accepted Answer

Replace $$x$$ with $$-x$$ and $$y$$ with $$-y.$$

Question 4

Given the equation $$2x - 3y = 6$$, what are the x- and y-intercepts?

Accepted Answer

x-intercept: $$(3, 0)$$, y-intercept: $$(0, -2)$$

Question 5

Which of the following equations is symmetric with respect to the y-axis?

Accepted Answer

$$y = x^2$

Question 6

If a graph is symmetric with respect to the x-axis, which of the following must be true for every point $$(x, y) on $$the graph?

Accepted Answer

$$(x, -y) is $$also on the graph.

Question 7

Which substitution would you use to test the equation $$y = x^3$ - 2$$ for y-axis symmetry?

Accepted Answer

Replace $$x$$ with $$-x.$$

Question 8

A real-world scenario: The path of a thrown ball is modeled by $$y = -x^2$ + 4. Is $$the path symmetric with respect to the y-axis?

Accepted Answer

Yes, because replacing $$x$$ with $$-x$$ gives the same equation.

Question 9

Which of the following equations is symmetric with respect to the origin?

Accepted Answer

$$y = x^3$

Question 10

Suppose you are analyzing the chemical reaction rate modeled by $$y = -2x. $$What type of symmetry does this equation have?

Accepted Answer

Origin symmetry

Question 11

If the equation $$y^2 = x$ is tested for symmetry, which of the following is true?

Accepted Answer

It is symmetric with respect to the x-axis.

Question 12

Which of the following best describes the symmetry of the equation $$y = x^2$ - 3$$?

Accepted Answer

Y-axis symmetry

Question 13

A medical researcher models the spread of a virus with $$y = -x^2$ + 5. $$What does the symmetry of this equation imply about the spread?

Accepted Answer

The spread is symmetric about the y-axis.

Question 14

Which of the following equations is NOT symmetric with respect to the y-axis, x-axis, or origin?

Accepted Answer

$$y = x + 1$$

Question 15

If you replace $$x$$ with $$-x in $$the equation $$y = x^2$ + 2$$, what do you get?

Accepted Answer

$$y = x^2$ + 2$$

Symmetry in Graphs: Intercepts and Testing for Symmetry

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