Q: A gym charges a $$40 sign-up fee and 25 $$per month. Write a function $$C(x)$$ for the total cost after $$x$$ months. What is the cost after 12 months?

$$C(12) = 40 + 25 \times 12 = 340$$

Question 1

Cameron’s annual zoo admission cost is modeled by $$y = 20x + 65$$, where $$x is $$the number of guests. What is the domain of this function in the context of the problem?

Accepted Answer

$$[0, \infty)$$

Question 2

Which of the following equations represents a function whose domain is $$[2, \infty)$$?

Accepted Answer

$$f(x) = \sqrt{x-2}$$

Question 3

A company’s revenue is modeled by $$R(x) = 50x - 200$$, where $$x is $$the number of units sold. What does $$R(0)$$ represent?

Accepted Answer

The revenue when no units are sold

Question 4

Given the function $$h(x) = 2x^2$ - x + 3$$, what is $$h(-3)$$?

Accepted Answer

$$h(-3) = 24$$

Question 5

Which of the following is the correct interval notation for the solution set $$\{x | x \leq -2\}$$?

Accepted Answer

$$(-\infty, -2]$$

Question 6

A gym charges a $$40 sign-up fee and 25 $$per month. Write a function $$C(x)$$ for the total cost after $$x$$ months. What is the cost after 12 months?

Accepted Answer

$$C(12) = 40 + 25 	imes 12 = 340$$

Question 7

Which of the following best describes the slope of the line passing through the points $$(2, 5)$$ and $$(3, 1)$$?

Accepted Answer

$$m = \frac{1-5}{3-2} = -4$$

Question 8

If $$f(x) = -x^2$ - 2x + 3$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 4]$$

Question 9

A city’s water usage decreased from 320 gallons/day in 2010 to 250 gallons/day in 2020. What is the average rate of change per year?

Accepted Answer

$$\frac{250 - 320}{2020 - 2010} = -7$$ gallons/year

Question 10

Which of the following is the correct domain for $$f(x) = \frac{1}{x+3}$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, \infty)$$

Question 11

A restaurant bill is $$152.26$$ after a $$15\%$$ gratuity is included. What was the cost of the meal before the tip?

Accepted Answer

$$\frac{152.26}{1.15} \approx 132.40$$

Question 12

Which of the following is NOT a function?

Accepted Answer

$$x = 2$$

Question 13

Solve for $$x$$: $$\frac{x}{6} = 1 - \frac{x}{4}$$

Accepted Answer

$$x = 2.4$$

Question 14

Which equation models the total cost $$y$$ for Plan B, where the monthly fee is $$20$$ plus $$5$$ per GB of data used $$x$$?

Accepted Answer

$$y = 20 + 5x$$

Question 15

Given the system: $$x - y = 5$$ and $$2x + y = 1$$, what is the solution?

Accepted Answer

$$(2, -3)$$

Question 16

A company manufactures earbuds with fixed costs of $$262,500$$ and variable cost $$23$$ per unit. If each earbud sells for $$98$$, what is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = 98x - (23x + 262,500)$$

Question 17

Which of the following best describes the solution set for $$-5x \u003c 20$$?

Accepted Answer

$$(-\infty, -4)$$

Question 18

If $$f(x) = x^3$ - x$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 19

Which of the following is the correct equation for a horizontal line passing through $$(6, -5)$$?

Accepted Answer

$$y = -5$$

College Algebra Study Guide: Graphs, Functions, and Linear Models

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