Question 1

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

Accepted Answer

The set of all input numbers of the function.

Question 2

Given $$f(x) = \dfrac{x(x-1)}{x-2}$$ and $$g(x) = x^2$, which of the following statements is true about their equality?

Accepted Answer

They are not equal for any $$x.$$

Question 3

What is the range of the function $$f(x) = 3x^2$ + 5$$?

Accepted Answer

$$[5, \infty)$$

Question 4

Find the domain of $$f(x) = \dfrac{x}{x^2$ - x - 2}.$$

Accepted Answer

$$x 
eq 2$$ and $$x 
eq -1$$

Question 5

Given $$g(x) = \sqrt{2x-1}$$, what is the domain of $$g$$?

Accepted Answer

$$x \geq \dfrac{1}{2}$$

Question 6

If $$f(x) = x^2$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Question 7

For $$f(x) = \dfrac{x}{3}$$, compute the difference quotient $$\dfrac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$\dfrac{1}{3}$$

Question 8

Which of the following is NOT a correct definition according to the study materials?

Accepted Answer

Domain: The set of all output numbers is the domain of the function.

Question 9

Suppose $$f(x) = x^2$ and g(x$$) = $$x^2$$ for all $$x in$$ $$\mathbb{R}. $$Are $$f$$ and $$g$$ equal?

Accepted Answer

Yes, because their domains and outputs are identical.

Question 10

A medical researcher models the dosage of a drug by $$d(t) = \dfrac{t}{t-5}$$, where $$t is $$time in hours. What is the domain of $$d$$?

Accepted Answer

$$t 
eq 5$$

Question 11

If $$f(x) = \sqrt{x-3}$$, which of the following describes the domain?

Accepted Answer

$$x \geq 3$$

Question 12

A function $$h(x) is $$defined as $$h(x) = \dfrac{x^2$ - 1}{x - 1}$$ for $$x 
eq 1. $$What is $$h(2)$$?

Accepted Answer

$$3$$

Question 13

Given $$f(x) = x^2$ and g(x$$) = $$x^2$$ for $$x \geq 0$$, are $$f$$ and $$g$$ equal?

Accepted Answer

No, because their domains are different.

Question 14

A chemical reaction rate is modeled by $$r(x) = \dfrac{x}{x^2$ - 4}. $$What values of $$x$$ are excluded from the domain?

Accepted Answer

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

Question 15

If $$f(x) = x^2$ and g(x$$) = $$x^2$$ for $$x \leq 1$$, which of the following is true?

Accepted Answer

They are equal only for $$x \leq 1.$$

Question 16

Find the value of the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$ for $$f(x) = 3x + 5.$$

Accepted Answer

$$3$$

Question 17

A function $$f is $$defined by $$f(x) = \dfrac{1}{x-3}. $$What is the domain of $$f$$?

Accepted Answer

$$x 
eq 3$$

Question 18

If $$f(x) = x^2$ and g(x$$) = $$x^2$$ for $$x 
eq 1$$, are $$f$$ and $$g$$ equal?

Accepted Answer

No, because their domains are different.

Question 19

A function $$f is $$defined as $$f(x) = \dfrac{x^2$ - 4}{x - 2}$$ for $$x 
eq 2. $$What is $$f(3)$$?

Accepted Answer

$$5$$

Functions: Definitions, Domains, and Difference Quotients in Precalculus

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