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 or touches the x-axis.

Question 2

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

Accepted Answer

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

Question 3

Which test would you use to determine if a graph is symmetric with respect to the y-axis?

Accepted Answer

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

Question 4

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

Accepted Answer

$$(-2, 5)$$

Question 5

For the equation $$y = x^3$, which of the following statements is true about its symmetry?

Accepted Answer

It is symmetric with respect to the origin.

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 $$y = 2x^2$ + 5$$?

Accepted Answer

$$y = 5$$

Question 8

A graph is symmetric with respect to the x-axis if:

Accepted Answer

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

Question 9

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

Accepted Answer

$$y = x^2$

Question 10

Given the equation $$x = y^2$, what is the shape of its graph?

Accepted Answer

A parabola opening to the right

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$$(-3, 7)$$

Question 13

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

Accepted Answer

$$y^2 = x$

Question 14

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

$$1.5$$, the initial height of the projectile

Question 15

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

Accepted Answer

$$y = x^3$

Question 16

Given the equation $$y = \frac{2x}{x^2$ + 1}$$, what is the y-intercept?

Accepted Answer

$$y = 0$$

Question 17

If a graph passes the test for symmetry with respect to the origin, which substitution produces an equivalent equation?

Accepted Answer

Replace $$x by$$ $$-x$$ and $$y by$$ $$-y$$

Question 18

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 19

A graph is said to have 'sufficient detail' when:

Accepted Answer

It shows enough of the graph so that the rest is an obvious continuation.

Question 20

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.

Graphs of Equations in Two Variables: Intercepts and Symmetry

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