Question 1

Refer to the first image (Graphs A, B, and C). Which of the following graphs represents a function, and why?

Accepted Answer

Graph A, because it passes the vertical line test.

Question 2

Given the function $$f(x) = x^2$ - 3x + 5$$, what is the value of $$f(-2)$$?

Accepted Answer

$$f(-2) = (-2)^2$ - 3(-2) + 5 = 4 + 6 + 5 = 15$$

Question 3

For the function $$h(t) = -16t^2$ + 48t + 5$$ modeling the height of a ball, what does $$h(0)$$ represent?

Accepted Answer

The initial height of the ball at time $$t = 0.$$

Question 4

Using Figure 2, what is the domain and range of the function $$f$$?

Accepted Answer

Domain: $$[-5, 5]$$, Range: $$[-2, 3]$$

Question 5

Refer to Figure 3. What is the value of $$h(-4)$$?

Accepted Answer

$$h(-4) = 2$$

Question 6

Which of the following functions is even?

Accepted Answer

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

Question 7

Evaluate the greatest integer function: $$	ext{int}(-0.5).$$

Accepted Answer

$$-1$$

Question 8

A wheelchair ramp rises 2.5 feet over a horizontal distance of 30 feet. What is the slope of the ramp in lowest terms?

Accepted Answer

$$\frac{2.5}{30} = \frac{1}{12}$$

Question 9

Given the line $$5x - 2y = 10$$, what is its slope?

Accepted Answer

Question 10

Which transformation describes $$g(x) = (x-3)^2$ + 2$$ relative to $$f(x) = x^2$?

Accepted Answer

Shift right 3 units and up 2 units.

Question 11

Let $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2. $$What is $$(f+g)(x)$$?

Accepted Answer

$$x^2 - 2$

Question 12

Given $$f(x) = \sqrt{x+4}$$ and $$g(x) = \sqrt{6-x}$$, what is the domain of $$f+g$$?

Accepted Answer

$$[-4, 2]$$

Question 13

If $$f(x) = 3x + 6$$ and $$g(x) = \frac{x-6}{3}$$, are $$f$$ and $$g$$ inverses of each other?

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x.$$

Question 14

Given the function $$f(x) = x^2$ + 1$$ for $$x \geq 0$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x-1}$$, domain $$[1, \infty)$$

Question 15

A bike rental shop charges a flat fee of $$8 plus 3 $$per hour. What is the function $$C(t)$$ for the cost of renting a bike for $$t$$ hours?

Accepted Answer

$$C(t) = 8 + 3t$$

Question 16

Given the graph in Figure 5, during which time interval is Maria not moving?

Accepted Answer

From 20 to 60 minutes

Question 17

Given the lines $$L_1$$ and $$L_2 in $$Figure 6, what is the point of intersection?

Accepted Answer

$$(1, 1)$$

Question 18

Which of the following graphs (from the fourth image) is an odd function?

Accepted Answer

Graph B

College Algebra Study Guide: Functions and Graphs (Sections 2.1–2.7)

Study Guide - Practice Questions