Question 1

Which of the following relations is NOT a function?

Accepted Answer

The set of ordered pairs $$\{(1,2), (1,3), (2,4)\}$$

Question 2

Given the function $$f(x) = \dfrac{2x}{x^2$-4}$$, what is the domain of $$f$$?

Accepted Answer

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

Question 3

Suppose $$g(x) = \sqrt{2x+1}. $$What is the domain of $$g$$?

Accepted Answer

$$[-\dfrac{1}{2}, \infty)$$

Question 4

Which of the following graphs does NOT represent a function?

Accepted Answer

A graph that crosses the y-axis three times at different y-values for the same x

Question 5

Given $$f(x) = |x|$$, which of the following statements is TRUE?

Accepted Answer

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

Question 6

For the function $$h(x) = x^3$ - 2x$$, determine whether $$h is $$even, odd, or neither.

Accepted Answer

Odd

Question 7

A temperature in degrees Celsius over a four-hour period is modeled by $$T(t) = t^2$ - 2t - 3$$, $$0 \leq t \leq 4. $$What is the average rate of change of temperature from $$t=1 to$$ $$t=4$$?

Accepted Answer

$$3$$

Question 8

Which of the following best describes the range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 9

Given the function $$f(x) = \dfrac{1}{1+x^2$}$$, which of the following is TRUE?

Accepted Answer

$$f is an $$even function

Question 10

Suppose $$f(x) is $$increasing on $$(-2,2)$$ and decreasing on $$(-\infty,-2)$$ and $$(2,\infty). $$What are the relative extrema?

Accepted Answer

Relative min at $$x=-2$$, relative max at $$x=2$$

Question 11

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

Accepted Answer

$$(x+1)^2$$

Question 12

A function $$f is $$defined by $$f(x) = \dfrac{1}{x-1}. $$What is the domain of $$f$$?

Accepted Answer

$$(-\infty, 1) \cup (1, \infty)$$

Question 13

Which of the following is the correct interpretation of the average rate of change of a function $$f on$$ $$[a, b]$$?

Accepted Answer

The slope of the line passing through $$(a, f(a))$$ and $$(b, f(b))$$

Question 14

Given $$f(x) = x^2$ - 4$$, for which values of $$x is$$ $$f(x) = 0$$?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 15

Which of the following is a real-world example of a function?

Accepted Answer

Assigning each person in a city their unique social security number

Question 16

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

Accepted Answer

$$1$$

Question 17

Which of the following statements about the vertical line test (VLT) is TRUE?

Accepted Answer

If every vertical line crosses the graph at most once, the graph is a function.

Question 18

Given the function $$f(x) = \sqrt{x-2}$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 19

Suppose the graph of a function $$f$$ has a gap at $$x=2$$ but is defined everywhere else. Which of the following is TRUE?

Accepted Answer

The domain of $$f is$$ $$(-\infty, 2) \cup (2, \infty)$$

Precalculus Study Notes: Functions, Domains, and Graphs (Chapter 2, Sections 2.4–2.9)

Study Guide - Practice Questions

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