$$f(g(2)) = 5 \times 5 + 6 = 31$$

Question 1

Which of the following points is located in Quadrant II of the rectangular coordinate system?

Accepted Answer

$$(-3, 5)$$

Question 2

Given the equation $$y = |x + 1|$$, which of the following tables correctly lists three points on its graph?

Accepted Answer

$$x = -1, y = 0; x = 0, y = 1; x = 1, y = 2$$

Question 3

For the function $$y = x^2$ - 2$$, what is the $$y-$$intercept?

Accepted Answer

$$y = -2$$

Question 4

A graph of a function passes through the points $$(0, 3)$$ and $$(2, 0). $$What are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$x = 2$$, $$y-$$intercept: $$y = 3$$

Question 5

Given the function $$f(x) = x^2$ - 2x + 7$$, what is $$f(-5)$$?

Accepted Answer

$$62$$

Question 6

Which of the following relations is NOT a function?

Accepted Answer

$$\{(6,1), (6,3), (6,2), (9,1)\}$$

Question 7

Which equation does NOT define $$y as a $$function of $$x$$?

Accepted Answer

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

Question 8

Given $$f(x) = x^2$ - 2x + 7$$, what is $$f(x+3)$$?

Accepted Answer

Question 9

Which graph passes the vertical line test and therefore represents a function?

Accepted Answer

A parabola opening upward

Question 10

For the function $$f(x) = 6x + 1$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$6$$

Question 11

Find the slope of the line passing through the points $$(4, -2)$$ and $$(1, 5).$$

Accepted Answer

$$-\frac{7}{3}$$

Question 12

Write the equation of a line in point-slope form passing through $$(1, 5)$$ with slope $$m = 2.$$

Accepted Answer

$$y - 5 = 2(x - 1)$$

Question 13

Which of the following lines is perpendicular to $$y = 4x - 2$$?

Accepted Answer

$$y = -\frac{1}{4}x + 3$$

Question 14

Given $$f(x) = x^2$ and g(x$$) = $$x^2 - 2$, how is the graph of g$ related to the graph of f$?

Accepted Answer

It is shifted downward by 2 units.

Question 15

Which transformation results in the graph of $$y = |x| + 4$$ from $$y = |x|$$?

Accepted Answer

Vertical shift upward by 4 units

Question 16

If $$f(x) = \sqrt{x}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 0$$

Question 17

Given $$f(x) = 5x + 6$$ and $$g(x) = 2x^2$ - x - 1$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 5 	imes 5 + 6 = 31$$

Question 18

Which of the following functions is even?

Accepted Answer

$$f(x) = 5x^4$ - 3x^2$ - 2$$

Question 19

What is the average rate of change of $$f(x) = x^2$ - 2x$$ from $$x_1 = 3$ to x_2$ = 6$$?

Accepted Answer

$$4$$

Graphs, Functions, and Linear Equations: Foundations of Precalculus

Study Guide - Practice Questions