Question 1

Which of the following best describes a function?

Accepted Answer

A relation in which each element in the domain corresponds to exactly one element in the range.

Question 2

Given the function $$g(x) = x^3$ - 4x$$, as shown in the first image, what is the range of $$g(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 3

Which of the following sets represents a relation that is NOT a function?

Accepted Answer

$$\{ (1, 2), (–3, 4), (–7, 2), (2, 8), (–3, 5) \}$$

Question 4

Using the vertical line test, which graph in the second image represents a function?

Accepted Answer

Graph (a)

Question 5

What is the domain of the function $$g(x) = x^3$ - 4x$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 6

If a function is defined by $$f(x) = \frac{1}{x-2}$$, what is its domain?

Accepted Answer

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

Question 7

Which of the following is the correct interval notation for all real numbers except $$x = 3$$?

Accepted Answer

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

Question 8

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

Accepted Answer

$$0$$

Question 9

Which of the following best describes the range of the function $$f(x) = \sqrt{x-1}$$?

Accepted Answer

$$[0, \infty)$$

Question 10

A function is given by the table: $$x: 5, 6, 7, 8$$; $$y: 1, 1, 1, 1. $$What is the range of this function?

Accepted Answer

$$\{1\}$$

Question 11

Which of the following is NOT a valid representation of a function?

Accepted Answer

A graph that fails the vertical line test

Question 12

If a function is defined by $$f(x) = \sqrt{9 - x^2$}$$, what is its domain?

Accepted Answer

$$[-3, 3]$$

Question 13

Which of the following is the implied domain for the function $$h(x) = \frac{1}{\sqrt{x-4}} in a $$real-world context?

Accepted Answer

$$(4, \infty)$$

Question 14

Given the function $$f(x) = x^2$ + 2x + 1$$, which of the following is the correct interval notation for its domain?

Accepted Answer

$$(-\infty, \infty)$$

Question 15

Which of the following statements is true about the function $$g(x) = x^3$ - 4x as $$shown in the first image?

Accepted Answer

The function passes the vertical line test everywhere.

Question 16

If a function is given verbally as 'the temperature $$T in $$degrees Celsius as a function of time $$t in $$hours,' which variable is the independent variable?

Accepted Answer

$$t$$

Question 17

Which of the following is the correct symbolic representation for the function 'the area $$A of a $$circle as a function of its radius $$r$$'?

Accepted Answer

$$A(r) = \pi r^2$

Question 18

Which of the following is the correct interval notation for the solution to $$x \u003e -2$$?

Accepted Answer

$$(-2, \infty)$$

Question 19

If $$f(x) = x^2$ - 4x + 3$$, what is $$f(1)$$?

Accepted Answer

$$-2$$

Question 20

Which of the following is NOT a possible range for a function $$f(x)$$?

Accepted Answer

$$[5, 2]$$

Functions and Their Representations: College Algebra Study Notes

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