Question 1

Given the points $$A(-2,1)$$ and $$B(3,4)$$, what is the distance between them?

Accepted Answer

$$\sqrt{34}$$

Question 2

Which of the following points lies in Quadrant III of the $$xy-$$coordinate plane?

Accepted Answer

$$(-2, -7)$$

Question 3

What is the midpoint of the line segment joining the points $$(5, 5)$$ and $$(3, 1)$$?

Accepted Answer

$$(4, 3)$$

Question 4

A triangle has vertices at $$A(-2,1)$$, $$B(3,1)$$, and $$C(2,3). Is $$this triangle a right triangle?

Accepted Answer

Yes, because $$a^2$$ + $$b^2$$ = $$c^2$$ for the side lengths.

Question 5

Which equation represents a graph that is symmetric about the $$y-$$axis?

Accepted Answer

$$y = x^2$

Question 6

For the function $$y = 2x^2$ - 1$$, which of the following statements is true?

Accepted Answer

The graph is symmetric about the $$y-$$axis.

Question 7

Find the $$x-$$intercepts of the equation $$y = x^2$ + 2x - 3.$$

Accepted Answer

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

Question 8

What is the slope of the line passing through the points $$(-1, -3)$$ and $$(4, 2)$$?

Accepted Answer

$$1$$

Question 9

A line has a slope of $$m = -\frac{4}{5}$$ and passes through the point $$(-2, 3). $$Which of the following points also lies on this line?

Accepted Answer

$$(3, -1)$$

Question 10

Which of the following equations is symmetric about the origin?

Accepted Answer

$$y = x^3$

Question 11

If a function $$f(x) is $$even, which of the following must be true for all $$x in $$its domain?

Accepted Answer

$$f(-x) = f(x)$$

Question 12

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 13

A real-world application: A drone flies from point $$A(2, 3) to $$point $$B(10, 15). $$What is the straight-line distance the drone travels?

Accepted Answer

$$\sqrt{164}$$

Question 14

Which of the following statements about the slope of a line is correct?

Accepted Answer

A line with a positive slope rises from left to right.

Question 15

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

Accepted Answer

$$3$$

Question 16

Which of the following equations is NOT symmetric about the $$y-$$axis?

Accepted Answer

$$y = x^3$

Question 17

If the midpoint of a line segment is $$(2, -1)$$ and one endpoint is $$(4, 3)$$, what is the other endpoint?

Accepted Answer

$$(0, -5)$$

Question 18

A function $$f(x) is $$odd if:

Accepted Answer

$$f(-x) = -f(x)$$

Question 19

Which of the following best describes the $$x-$$intercepts of the quadratic $$y = 2x^2$ - 1$$?

Accepted Answer

$$x = \pm \frac{1}{\sqrt{2}}$$

Question 20

A real-world scenario: A cable is stretched between two towers at $$(0,0)$$ and $$(6,8). $$What is the length of the cable?

Accepted Answer

$$10$$

Precalculus Foundations: Coordinate Geometry, Symmetry, and Graphs

Study Guide - Practice Questions