Question 1

Which of the following relations is NOT a function?

Accepted Answer

A relation where the ordered pairs are $$(1,2), (1,3), (2,4).$$

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(4)$$?

Accepted Answer

$$29$$

Question 3

What is the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$x \geq 2$$

Question 4

A population of bacteria grows according to the function $$P(t) = 500 + 20t$$, where $$t is $$time in hours. What is the average rate of change of the population from $$t = 2 to$$ $$t = 5$$?

Accepted Answer

$$20$$

Question 5

Find the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13).$$

Accepted Answer

$$2$$

Question 6

Which of the following is the equation of a line parallel to $$y = 3x - 7$$ and passing through the point $$(1, 2)$$?

Accepted Answer

$$y = 3x - 1$$

Question 7

Solve the inequality $$2x - 5 \u003c 9$$ and express the answer in interval notation.

Accepted Answer

Question 8

A car travels at a constant rate of $$60$$ miles per hour. How far will it travel in $$2.5$$ hours?

Accepted Answer

$$150$$ miles

Question 9

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 2x-1 & x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-1$$

Question 10

Which of the following is the correct set builder notation for the domain of $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$\{ x \mid x 
eq 4 \}$$

Question 11

If $$y$$ varies directly with $$x$$ and $$y = 12$$ when $$x = 3$$, what is the value of $$y$$ when $$x = 8$$?

Accepted Answer

$$32$$

Question 12

Which of the following describes the graph of $$f(x) = |x|$$?

Accepted Answer

A V-shaped graph opening upwards

Question 13

Find the $$x-$$intercept of the line $$y = 4x - 8.$$

Accepted Answer

$$x = 2$$

Question 14

Which of the following lines is perpendicular to $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$y = 2x - 1$$

Question 15

A company’s cost function is $$C(x) = 200 + 15x$$, where $$x is $$the number of units produced. What is the cost to produce $$10$$ units?

Accepted Answer

$$350$$

Question 16

Given the function $$f(x) = x^2$ - 4x + 3$$, find the zeros of the function.

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 17

For the function $$f(x) = x^3$, which of the following statements is true?

Accepted Answer

The function is increasing for all real values of $$x$$

Question 18

A piecewise function is defined as $$f(x) = \begin{cases} 2x & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}. $$What is $$f(1)$$?

Accepted Answer

$$1$$

Question 19

Which of the following is the correct interval notation for the domain of $$f(x) = \sqrt{9 - x}$$?

Accepted Answer

$$(-\infty, 9]$$

Question 20

A line passes through $$(0, 5)$$ and $$(4, 13). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 2x + 5$$

College Algebra Study Guide: Functions, Graphs, and Linear Equations (Sections 1.3–2.4)

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