Question 1

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

Accepted Answer

$$\{x \mid x \geq 2\}$$

Question 2

Given the function $$f(x) = \frac{1}{x-1}$$, which value is NOT in the domain of $$f$$?

Accepted Answer

$$x = 1$$

Question 3

A function is defined by the set of ordered pairs $$\{(-1, 4), (0, 3), (1, 4), (2, -2)\}. $$What is the range of this function?

Accepted Answer

$$\{-2, 3, 4\}$$

Question 4

Which of the following graphs passes the vertical line test and therefore represents a function?

Accepted Answer

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

Question 5

If $$g(x) = x^2$ - 2x$$, what is $$g(-1)$$?

Accepted Answer

$$g(-1) = (-1)^2$ - 2(-1) = 1 + 2 = 3$$

Question 6

Which of the following is the correct symbolic representation for the function that describes the distance (in miles) from a lightning bolt as a function of the time (in seconds) between seeing lightning and hearing thunder?

Accepted Answer

$$f(x) = \frac{x}{5}$$

Question 7

Which of the following is an example of set-builder notation for all real numbers $$y$$ such that $$1 \u003c y \u003c 5$$?

Accepted Answer

$$\{y \mid 1 \u003c y \u003c 5\}$$

Question 8

A function $$f is $$defined by $$f(x) = x^2$ + 1. $$Which of the following is the correct numerical representation for $$x = -2$$?

Accepted Answer

$$f(-2) = 5$$

Question 9

Which of the following statements is TRUE about the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

The domain is $$[2, \infty).$$

Question 10

Which of the following diagrams does NOT represent a function?

Accepted Answer

A diagram where one input is paired with two different outputs.

Question 11

Given the function $$f(x) = x^2$ + 1$$, what is the graphical representation of $$f$$?

Accepted Answer

A parabola opening upwards with vertex at $$(0, 1).$$

Question 12

Which of the following is NOT a valid way to represent a function?

Accepted Answer

Randomly pairing outputs to inputs

Question 13

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

Accepted Answer

$$[-1, \infty)$$

Question 14

Which of the following best describes the relationship between domain and range?

Accepted Answer

The domain is the set of all possible inputs, and the range is the set of all possible outputs.

Question 15

Suppose $$y is a $$function of $$x$$ given by $$y = x^2$ - 2. $$Which of the following is true?

Accepted Answer

Each $$x$$ value determines exactly one $$y$$ value.

Question 16

Which of the following is the correct interval notation for the set $$\{x \mid x \geq 2\}$$?

Accepted Answer

$$[2, \infty)$$

Question 17

If a vertical line intersects a graph at more than one point, what does this indicate?

Accepted Answer

The graph does not represent a function.

Question 18

Given the function $$f(x) = x^2$ + 1$$, what is $$f(0)$$?

Accepted Answer

$$f(0) = 1$$

Question 19

Which of the following is a correct verbal representation of the function $$f(x) = x^2$ + 1$$?

Accepted Answer

Square the input $$x$$ and add 1 to produce the output.

Functions and Their Representations: College Algebra Study Notes

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