Question 1

Which of the following best describes the x-intercept of a graph?

Accepted Answer

The x-coordinate of a point where the graph crosses the x-axis.

Question 2

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

Accepted Answer

$$x = -1$$ and $$x = 3$$

Question 3

Which test would you use to determine if the graph of $$y = x^3$ is symmetric with respect to the origin?

Accepted Answer

Replace $$x by$$ $$-x$$ and $$y by$$ $$-y in $$the equation.

Question 4

If a graph is symmetric with respect to the y-axis and contains the point $$(3, 7)$$, which other point must also be on the graph?

Accepted Answer

$$(-3, 7)$$

Question 5

For the equation $$x = y^2$, which of the following statements is true?

Accepted Answer

The graph is symmetric with respect to the x-axis.

Question 6

Which of the following points is on the graph of $$4x - 3y = -24$$?

Accepted Answer

$$(-9, -4)$$

Question 7

What is the y-intercept of the equation $$y = 2x^3$ + 5$$?

Accepted Answer

$$(0, 5)$$

Question 8

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

Accepted Answer

$$(x, -y)$$

Question 9

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

Accepted Answer

$$y = x^2$

Question 10

Suppose you are graphing $$y = x^2$ by plotting points. Which of the following sets of points would you plot to show the basic shape of the graph?

Accepted Answer

$$(0, 0), (1, 1), (2, 4), (-1, 1), (-2, 4)$$

Question 11

Which of the following best describes the solution set of an equation in two variables?

Accepted Answer

The set of all points $$(x, y)$$ that satisfy the equation.

Question 12

If the graph of an equation is symmetric with respect to the origin and contains the point $$(2, -5)$$, which other point must also be on the graph?

Accepted Answer

$$(-2, 5)$$

Question 13

Which of the following is the correct procedure to find the y-intercept of the graph of an equation?

Accepted Answer

Let $$x = 0$$ and solve for $$y.$$

Question 14

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

Accepted Answer

$$y^2 = x$

Question 15

A real-world application: The height $$h (in $$meters) of a projectile at time $$t (in $$seconds) is given by $$h = -4.9t^2$ + 20t + 1.5. $$What is the y-intercept, and what does it represent?

Accepted Answer

$$(0, 1.5)$$; the initial height of the projectile.

Question 16

Which of the following is NOT a correct method for graphing an equation in two variables?

Accepted Answer

Using only the intercepts to draw the entire graph.

Question 17

Given the equation $$y = x^2$ - 2x - 3$$, what is the y-intercept?

Accepted Answer

$$(0, -3)$$

Question 18

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

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 19

If a graph passes the test for symmetry with respect to the origin, which transformation leaves the graph unchanged?

Accepted Answer

Replacing $$(x, y)$$ with $$(-x, -y).$$

Graphs of Equations in Two Variables: Intercepts and Symmetry

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