Question 1

Which of the following is the standard form of the equation of a circle with center at $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x - h)^2$ + (y - k)^2$ = r^2$

Question 2

Given the points $$A(2, 3)$$ and $$B(6, 11)$$, what is the slope of the line passing through these points?

Accepted Answer

$$\frac{11 - 3}{6 - 2} = 2$$

Question 3

Which of the following equations represents a vertical line passing through the point $$(4, -2)$$?

Accepted Answer

$$x = 4$$

Question 4

If a line has a slope of $$-\frac{3}{4}$$ and passes through the point $$(0, 5)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = -\frac{3}{4}x + 5$$

Question 5

Which of the following is the general form of the equation of a line?

Accepted Answer

$$Ax + By + C = 0$$

Question 6

A circle has the equation $$(x - 2)^2$ + (y + 3)^2$ = 25. $$What are the center and radius of the circle?

Accepted Answer

Center $$(2, -3)$$, radius $$5$$

Question 7

Which of the following best describes the graph of $$y = |x|$$?

Accepted Answer

A V-shaped graph opening upwards

Question 8

Given the function $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$\{x \mid x 
eq 2\}$$

Question 9

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 10

Which of the following is NOT a function?

Accepted Answer

A relation where one $$x-$$value is paired with two different $$y-$$values

Question 11

Given the function $$f(x) = \sqrt{x-1}$$, what is the range of $$f$$?

Accepted Answer

$$\{y \mid y \geq 0\}$$

Question 12

A line passes through $$(1, 2)$$ and is perpendicular to the line $$y = 3x + 4. $$What is the equation of the line?

Accepted Answer

$$y - 2 = -\frac{1}{3}(x - 1)$$

Question 13

Which of the following best describes the graph of $$y = x^2$?

Accepted Answer

A parabola opening upwards

Question 14

If $$f(x) = 2x + 3$$ and $$f(a) = 11$$, what is the value of $$a$$?

Accepted Answer

$$4$$

Question 15

Which of the following is the correct definition of the range of a function?

Accepted Answer

The set of all possible output values

Question 16

Given the function $$f(x) = x^2$ - 4x + 3$$, for which value(s) of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 17

Which of the following statements is true about the vertical line test?

Accepted Answer

If any vertical line crosses the graph more than once, it is not a function.

Question 18

If $$f(x) = x^2$ and g(x) = 2x$, what is f(g(3$$))$$?

Accepted Answer

$$36$$

Question 19

Which of the following is the equation of a horizontal line passing through $$(0, -5)$$?

Accepted Answer

$$y = -5$$

Question 20

Given the relation $$R = \{(1, 2), (2, 4), (3, 6), (4, 8)\}$$, what is the range of $$R$$?

Accepted Answer

$$\{2, 4, 6, 8\}$$

Precalculus Study Guide: Graphs, Functions, and Analytic Geometry

Study Guide - Practice Questions