Question 1

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

Accepted Answer

All possible inputs for which the function is defined.

Question 2

Given the function $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$x 
eq 2$$

Question 3

Which interval notation correctly represents all real numbers between 2 and 5, inclusive?

Accepted Answer

$$[2, 5]$$

Question 4

If $$g(x) = \sqrt{x-3}$$, what is the domain of $$g$$?

Accepted Answer

$$x \geq 3$$

Question 5

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

Accepted Answer

Graph of the range

Question 6

For the function $$h(x) = \frac{1}{x^2$-9}$$, which values must be excluded from the domain?

Accepted Answer

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

Question 7

Which of the following describes the process of finding the domain by looking at 'trouble points'?

Accepted Answer

Identifying where the function is not defined, such as division by zero or negative square roots.

Question 8

Given $$k(x) = \sqrt{x^2$-4}$$, what is the domain of $$k$$?

Accepted Answer

$$x \leq -2 or$$ $$x \geq 2$$

Question 9

If a function $$f(x) is $$defined for all real numbers except $$x = 0$$, how would you write its domain in interval notation?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 10

Which transformation would shift the graph of $$y = |x|$$ two units to the right?

Accepted Answer

$$y = |x-2|$$

Question 11

A function $$f(x) is $$defined as $$f(x) = \frac{1}{x^2$-1}. $$Which of the following is the correct domain?

Accepted Answer

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

Question 12

Which of the following is the correct interval notation for all real numbers except $$x = 4$$?

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 13

If $$f(x) = \sqrt{5-x}$$, what is the domain of $$f$$?

Accepted Answer

$$x \leq 5$$

Question 14

Which of the following best describes the effect of replacing $$x$$ with $$x-h in $$the function $$f(x)$$?

Accepted Answer

It shifts the graph $$h$$ units to the right.

Question 15

Given $$f(x) = x^2$ and g(x) = f(x-3$$)$$, what is the vertex of g(x$$)$$?

Accepted Answer

$$(3, 0)$$

Functions and Their Domains: College Algebra Study Notes

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