Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{2x+5}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 2

Given the function $$f(x) = \sqrt{x-4}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 3

Which of the following equations does NOT represent a function?

Accepted Answer

$$x^2$$ + $$y^2 = 9$

Question 4

If $$f(x) = 3x - 4$$, what is $$f(-2)$$?

Accepted Answer

$$-10$$

Question 5

A business buys baskets at $$8 each if buying less than 100, 7 $$each for 100 to 500, and $$6 each for more than 500. Which of the following is the correct piecewise cost function C(n$$)$$ for n$ baskets?

Accepted Answer

$$C(n) = \begin{cases} 8n, & n  500 \end{cases}$$

Question 6

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 7

Given $$f(x) = x^2$ - 4x + 7$$, find the average rate of change from $$x = 1 to$$ $$x = 5.$$

Accepted Answer

$$-2$$

Question 8

If $$f(x) = 2x + 3$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$11$$

Question 9

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

Accepted Answer

$$y = 2x - 1$$

Question 10

Suppose you buy a $$24,000 car that depreciates 3$$,000 each year. What is the value of the car after 3.5 years?

Accepted Answer

$$13,500$$

Question 11

What is the inverse of the function $$f(x) = 2x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-7}{2}$$

Question 12

Given points $$(3, 0)$$ and $$(-2, 4)$$, what is the midpoint?

Accepted Answer

$$(0.5, 2)$$

Question 13

Which transformation will shift the graph of $$f(x) = x^2$ to the right by 3 units?

Accepted Answer

$$f(x-3)$$

Question 14

If $$f(x) = |x|$$, which of the following is the graph of $$-f(x)$$?

Accepted Answer

A reflection of $$f(x)$$ over the x-axis

Question 15

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 16

Which of the following is the general form of a line?

Accepted Answer

$$Ax + By = C$$

Question 17

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

Accepted Answer

$$f(x) is an $$odd function

Question 18

What is the slope of the line passing through the points $$(2, 5)$$ and $$(0, -7)$$?

Accepted Answer

$$6$$

Question 19

Which of the following is the correct formula for the distance between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 20

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f + g)(2$$)$$?

Accepted Answer

$$7$$

College Algebra: Functions, Linear Equations, and Transformations

Study Guide - Practice Questions

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