Question 1

Which of the following graphs represents a function?

Accepted Answer

A graph where every vertical line touches the curve at most once.

Question 2

Given the function $$f(x) = x^2$ - 6x + 1$$ and $$g(x) = 2x - 1$$, what is $$3f(x) - 2g(x)$$?

Accepted Answer

$$3x^2 - 22x + 5$

Question 3

What is the domain of the function $$f(x) = \sqrt{x - 4}$$?

Accepted Answer

$$[4, \infty)$$

Question 4

If $$f(x) = 2x + 3$$ and $$g(x) = x^2$ - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$2(x^2 - 1) + 3$

Question 5

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = 0.195x + 12$$, where $$x is $$the number of months since January 2019. What is the average rate of change in revenue from January 2019 ($$x = 0) to $$December 2020 ($$x = 24$$)?

Accepted Answer

$$0.195$$ thousand dollars per month

Question 6

Which transformation shifts the graph of $$f(x) up by 5 $$units?

Accepted Answer

$$f(x) + 5$$

Question 7

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

Accepted Answer

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

Question 8

Which of the following intervals describes where the function $$f(x) is $$increasing if the graph goes up from left to right between $$x = -2$$ and $$x = 4$$?

Accepted Answer

$$(-2, 4)$$

Question 9

If $$f(x)$$ passes the horizontal line test, what property does $$f(x)$$ have?

Accepted Answer

It is a one-to-one function.

Question 10

Given $$f(x) = |x - 1|$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 11

A piecewise function is defined as $$f(x) = \begin{cases} 3 & x \u003c -1 \ x^2$ & -1 \leq x \u003c 1 \ x + 1 & x \geq 1 \end{cases}. $$What is $$f(0)$$?

Accepted Answer

$$0$$

Question 12

Which of the following is the correct point-slope form for a line passing through $$(2, 5)$$ with slope $$-3$$?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 13

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

Accepted Answer

$$\sqrt{x} + x^2$ + 3$$

Question 14

Which of the following is NOT a common mistake to avoid when working with functions and their domains?

Accepted Answer

Using correct sign errors in transformations

Question 15

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

Accepted Answer

$$9$$

Question 16

Which interval notation correctly represents all real numbers except $$x = 2$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 17

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

Accepted Answer

$$3x^3$$ - $$2x^2$$

Question 18

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

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 19

If $$f(x) = \frac{1}{x - 3}$$, what is the domain of $$f(x)$$?

Accepted Answer

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

Precalculus Study Guide: Functions, Graphs, Lines, Transformations, Operations, and Inverses (MAT 171 Sections 1.1–1.8)

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