Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(-9, -5), (9, 5), (2, 4)\}$$

Question 2

Given the function $$f(x) = 2x^2$ - x + 3$$, what is $$f(-7)$$?

Accepted Answer

$$108$$

Question 3

Which statement best describes the vertical line test for functions?

Accepted Answer

A graph is a function if every vertical line crosses the graph at most once.

Question 4

For the function $$h(x) = \dfrac{3x - x + 7}{x^2$ + 2x - 3}$$, which values must be excluded from the domain?

Accepted Answer

$$x = -3$$ and $$x = 1$$

Question 5

If $$f(x) = \sqrt{x+4}$$, what is the domain of $$f$$?

Accepted Answer

$$[-4, \infty)$$

Question 6

A chemical process is modeled by $$f(x) = x^2$ - 6. If $$the input $$x$$ represents the temperature in degrees Celsius, what is the output when the temperature is $$-3$$ degrees?

Accepted Answer

$$3$$

Question 7

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible outputs.

Question 8

Given $$f(x) = 2x^2$ - x + 3$$, find $$f(a-4) in $$terms of $$a.$$

Accepted Answer

$$2a^2 - 17a + 39$

Question 9

A hospital monitors a patient’s blood sugar using the function $$g(x) = \dfrac{1}{x-3}$$, where $$x is $$the time in hours after a meal. For which value of $$x is$$ $$g(x)$$ undefined?

Accepted Answer

$$x = 3$$

Question 10

Which of the following is a correct interpretation of $$f(x) in $$function notation?

Accepted Answer

The value of $$f at$$ $$x.$$

Question 11

A function $$f is $$defined by $$f(x) = x^2$ - x. $$What is $$f(5)$$?

Accepted Answer

$$20$$

Question 12

Which of the following graphs could NOT represent a function?

Accepted Answer

A graph where a vertical line crosses the graph twice.

Question 13

If a relation has two ordered pairs with the same first coordinate but different second coordinates, what can you conclude?

Accepted Answer

The relation is not a function.

Question 14

A company models its profit by $$P(x) = \sqrt{x+4}$$, where $$x is $$the number of products sold. What is the minimum number of products that must be sold for $$P(x) to be $$defined?

Accepted Answer

$$x = -4$$

Question 15

Given the function $$f(x) = \dfrac{1}{x-3}$$, which of the following statements is true?

Accepted Answer

$$f(3) is $$undefined$

Question 16

Which of the following best describes the domain of a function?

Accepted Answer

The set of all possible inputs.

Question 17

If $$f(x) = x^2$ - 6$$, estimate the range of $$f$$ for all real $$x.$$

Accepted Answer

$$[-6, \infty)$$

Question 18

A relation is given by $$\{(2, 5), (5, 7), (0, 1), (4, -2)\}. $$What is the domain?

Accepted Answer

$$\{2, 5, 0, 4\}$$

Question 19

Which of the following is true about functions and relations?

Accepted Answer

Every function is a relation.

Precalculus Study Notes: Functions and Their Graphs

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