Q: What is the cost of a 42-mile ride with the rideshare service that charges $$C(m) = 1.75m + 3.50$$? A) $$C(42) = 1.75 \times 42 + 3.50 = 76.00 B$$) $$C(42) = 1.75 \times 42 + 3.50 = 76.50 C$$) $$C(42) = 1.75 \times 42 = 73.50 D$$) $$C(42) = 1.75 + 3.50 = 5.25$$

D) $$C(42) = 1.75 \times 42 + 3.50 = 76.00$$

Question 1

Given the mapping diagram below, is the relation a function? What are the domain and range?

[Image: Mapping diagram with arrows from 8, 6, 4, 2 to 1, 3, 5]

A) Yes, Domain: $$\{2, 4, 6, 8\}$$, Range: $$\{1, 3, 5\}
B) No$$, Domain: $$\{1, 3, 5\}$$, Range: $$\{2, 4, 6, 8\}
C) $$Yes, Domain: $$\{1, 3, 5\}$$, Range: $$\{2, 4, 6, 8\}
D) No$$, Domain: $$\{2, 4, 6, 8\}$$, Range: $$\{1, 3, 5\}$$

Accepted Answer

A) Yes, Domain: $$\{2, 4, 6, 8\}$$, Range: $$\{1, 3, 5\}$$

Question 2

Consider the graph of a circle centered at the origin with radius 3. Is this relation a function? What is the domain and range?

A) Yes, Domain: $$[-3, 3]$$, Range: $$[-3, 3]
B) No$$, Domain: $$[-3, 3]$$, Range: $$[-3, 3]
C) $$Yes, Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)
D) No$$, Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Accepted Answer

B) No, Domain: $$[-3, 3]$$, Range: $$[-3, 3]$$

Question 3

Given the piecewise linear graph shown, what is the domain and range of the function?

A) Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)
B) $$Domain: $$(-\infty, \infty)$$, Range: $$[2, 6]
C) $$Domain: $$(-\infty, \infty)$$, Range: $$(-8, 6]
D) $$Domain: $$[0, 10]$$, Range: $$[0, 10]$$

Accepted Answer

C) Domain: $$(-\infty, \infty)$$, Range: $$(-8, 6]$$

Question 4

Which of the following equations represents a line with slope $$\frac{3}{4}$$ and $$y-$$intercept $$7$$?

A) $$y = \frac{3}{4}x + 7
B$$) $$y = 7x + \frac{3}{4}
C$$) $$y = \frac{4}{3}x + 7
D$$) $$y = 3x + 4$$

Accepted Answer

A) $$y = \frac{3}{4}x + 7$$

Question 5

Given the table of values:

| x | y  |
|---|----|
| 1 | 1.5|
| 3 | 0.5|
| 6 | -1 |
|10 | -3 |

What is the slope of the linear function that fits this data?

A) $$m = -0.4
B$$) $$m = 0.5
C$$) $$m = -1
D$$) $$m = 2$$

Accepted Answer

A) $$m = -0.4$$

Question 6

Which of the following lines is steeper: $$y = \frac{1}{2}x - 7 or$$ $$y = 3x + 5$$? Why?

A) $$y = \frac{1}{2}x - 7 is $$steeper because $$\frac{1}{2} \u003e 3
B$$) $$y = 3x + 5 is $$steeper because $$3 \u003e \frac{1}{2}
C$$) $$y = \frac{1}{2}x - 7 is $$steeper because $$-7 \u003e 5
D) $$Both lines have the same steepness

Accepted Answer

B) $$y = 3x + 5 is $$steeper because $$3 \u003e \frac{1}{2}$$

Question 7

Given $$f(x) = 3x - 2$$, $$g(x) = \frac{2}{3}x^2$, and h(x$$) = \sqrt{x}$$, what is (g+f)(3$$)$$?

A) g(3) + f(3) = 6 + 7 = 13$
B) g(3) + f(3) = 6 + 1 = 7$
C) g(3) + f(3) = 2 + 7 = 9$
D) g(3) + f(3) = 3 + 2 = 5$

Accepted Answer

A) $$g(3) + f(3) = 6 + 7 = 13$$

Question 8

What is the domain of the function $$h(x) = \sqrt{x}$$?

A) $$(-\infty, \infty)
B$$) $$[0, \infty)
C$$) $$(-\infty, 0]
D$$) $$(0, \infty)$$

Accepted Answer

B) $$[0, \infty)$$

Question 9

A rideshare service charges a flat pick-up fee of $$3.50 plus 1.75 $$for every mile traveled. Which linear function models the total cost $$C(m)$$ for $$m$$ miles?

A) $$C(m) = 1.75m + 3.50
B$$) $$C(m) = 3.50m + 1.75
C$$) $$C(m) = 1.75 + 3.50m
D$$) $$C(m) = 3.50m - 1.75$$

Accepted Answer

A) $$C(m) = 1.75m + 3.50$$

Question 10

A food truck owner purchases a commercial espresso machine for $$6,200. The machine depreciates at a constant rate of 450 $$per year. What is the linear model $$V(t)$$ for the value after $$t$$ years?

A) $$V(t) = 6200 - 450t
B$$) $$V(t) = 450t + 6200
C$$) $$V(t) = 6200 + 450t
D$$) $$V(t) = 450 - 6200t$$

Accepted Answer

A) $$V(t) = 6200 - 450t$$

Question 11

Given $$f(x) = x^2$ - 1$$, is $$f(x) a $$linear function? What is $$f(-2)$$?

A) Yes, $$f(-2) = 3
B) No$$, $$f(-2) = 3
C) $$Yes, $$f(-2) = -3
D) No$$, $$f(-2) = -3$$

Accepted Answer

B) No, $$f(-2) = 3$$

Question 12

Are the lines $$2y = 3x + 2$$ and $$2x + 4y = 5$$ parallel, perpendicular, or neither?

A) Parallel
B) Perpendicular
C) Neither
D) Coinciding

Accepted Answer

C) Neither

Question 13

If $$f(x) = 3x - 2$$ and $$g(x) = \frac{2}{3}x^2$, what is f(g(x$$))$$?

A) f(g(x)) = 3$$\left(\frac{2}{3}$$x^2$$\right) - 2$$
B) f(g(x$$)) = $$2x^2 - 2$
C) f(g(x$$)) = $$3x^2 - 2$
D) f(g(x$$)) = $$2x^2 + 3$

Accepted Answer

A) $$f(g(x)) = 3\left(\frac{2}{3}x^2$\right) - 2$$

Question 14

A person burns 1,300 calories daily at rest and 7 calories per minute of exercise. Write a linear equation for total calories burned $$y$$ after $$x$$ minutes of exercise.

A) $$y = 1300 + 7x
B$$) $$y = 7x - 1300
C$$) $$y = 1300x + 7
D$$) $$y = 7x$$

Accepted Answer

A) $$y = 1300 + 7x$$

Question 15

What is the cost of a 42-mile ride with the rideshare service that charges $$C(m) = 1.75m + 3.50$$?

A) $$C(42) = 1.75 	imes 42 + 3.50 = 76.00
B$$) $$C(42) = 1.75 	imes 42 + 3.50 = 76.50
C$$) $$C(42) = 1.75 	imes 42 = 73.50
D$$) $$C(42) = 1.75 + 3.50 = 5.25$$

Accepted Answer

D) $$C(42) = 1.75 	imes 42 + 3.50 = 76.00$$

Functions, Domain, and Range – Intermediate Algebra Study Guide

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