Question 1

Which of the following relations is a function?

Accepted Answer

$$\{(0,1), (1,2), (2,3)\}$$

Question 2

Given the equation $$y = 2x + 5$$, is this a function? If so, what is $$f(3)$$?

Accepted Answer

Function; $$f(3) = 11$$

Question 3

Which of the following graphs represents a function?

Accepted Answer

A parabola opening upwards

Question 4

A relation is given by the set $$\{(-2, 4), (0, 1), (3, 7)\}. $$What are the inputs and outputs?

Accepted Answer

Inputs: $$\{-2,0,3\}$$; Outputs: $$\{4,1,7\}$$

Question 5

Which of the following best describes the Vertical Line Test?

Accepted Answer

If any vertical line crosses the graph more than once, it is not a function.

Question 6

Given the equation $$x^2$$ + $$y^2 = 16$, is this a function?

Accepted Answer

No, because some $$x$$ values correspond to multiple $$y$$ values.

Question 7

Find the domain of the function $$f(x) = \sqrt{x+4}. $$Express your answer in interval notation.

Accepted Answer

$$[-4, \infty)$$

Question 8

Find the domain of the function $$f(x) = \dfrac{1}{x^2$ - 5x + 6}. $$Express your answer in interval notation.

Accepted Answer

$$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$$

Question 9

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward from the ground is given by $$h(t) = -4.9t^2$ + 20t. $$What is the domain of this function in the context of the problem?

Accepted Answer

$$[0, 4.08]$$

Question 10

Given the function $$f(x) = \sqrt{9 - x^2$}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, 3]$$

Question 11

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 12

If $$f(x) = \dfrac{1}{x-2}$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty) \setminus \{0\}$$

Question 13

Given the function $$f(x) = \sqrt{x-1}$$, for which $$x is$$ $$f(x)$$ defined?

Accepted Answer

$$x \geq 1$$

Question 14

A medical test result is modeled by $$f(t) = 100e$$^{-0.05t}$$, where t$ is time in hours. What is the range of f(t$$)$$?

Accepted Answer

$$(0, 100]$$

Question 15

Which of the following statements is true about the function $$f(x) = \dfrac{1}{x}$$?

Accepted Answer

The range is $$(-\infty, 0) \cup (0, \infty)$$

Question 16

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

Accepted Answer

$$[ -1, \infty )$$

Question 17

Which of the following best describes the domain of $$f(x) = \dfrac{1}{x^2$ - 1}$$?

Accepted Answer

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

Question 18

A chemical reaction's temperature $$T (in$$ $$^\circC) $$over time $$t (in $$minutes) is modeled by $$T(t) = 5t + 20$$ for $$0 \leq t \leq 10. $$What is the range of $$T$$?

Accepted Answer

$$[20, 70]$$

Question 19

Which of the following is the correct interval notation for all real numbers except $$x = 2$$ and $$x = 5$$?

Accepted Answer

$$(-\infty, 2) \cup (2, 5) \cup (5, \infty)$$

Relations, Functions, Domain, and Range in College Algebra

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