Question 1

Which of the following best describes the domain and range of the constant function $$y = c$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$\{c\}$$

Question 2

For the identity function $$y = x$$, which of the following statements is true?

Accepted Answer

It is increasing on $$(-\infty, \infty).$$

Question 3

What is the range of the absolute value function $$y = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 4

On which interval is the absolute value function $$y = |x|$$ decreasing?

Accepted Answer

$$(-\infty, 0)$$

Question 5

Which of the following is the domain of the square root function $$y = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 6

For the cubic function $$y = x^3$, which statement is correct?

Accepted Answer

It is increasing on $$(-\infty, \infty).$$

Question 7

What is the range of the cubic root function $$y = \sqrt[3]{x}$$?

Accepted Answer

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

Question 8

Consider the piecewise function $$f(x) = \begin{cases} 2x & 	ext{if } x \leq 1 \ 2 & 	ext{if } x \u003e 1 \end{cases}. $$What is the value of $$f(-2)$$?

Accepted Answer

$$-4$$

Question 9

For the piecewise function $$f(x) = \begin{cases} x^2$ & 	ext{if } x \geq 0 \ -x-2 & 	ext{if } x \u003c 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-5$$

Question 10

Which function has a domain of $$(-\infty, \infty)$$ and a range of $$(-\infty, \infty)$$?

Accepted Answer

Identity function $$y = x$$

Question 11

Which function is increasing on $$(0, \infty)$$ and decreasing on $$(-\infty, 0)$$?

Accepted Answer

Absolute value function $$y = |x|$$

Question 12

If $$f(x) = \sqrt{x}$$, what is $$f(16)$$?

Accepted Answer

$$4$$

Question 13

Which function is not defined for negative $$x$$ values?

Accepted Answer

Square root function $$y = \sqrt{x}$$

Question 14

For the function $$y = |x|$$, what is the value of $$y$$ when $$x = -7$$?

Accepted Answer

$$7$$

Question 15

Which of the following functions is constant for all $$x$$?

Accepted Answer

Constant function $$y = c$$

Question 16

For the piecewise function $$f(x) = \begin{cases} 2x & x \leq 1 \ 2 & x \u003e 1 \end{cases}$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 2]$$

Question 17

Which function's graph has a sharp 'corner' at $$x = 0$$?

Accepted Answer

Absolute value function $$y = |x|$$

Question 18

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

Accepted Answer

$$-8$$

Question 19

Which function is increasing for all $$x$$ and has both domain and range $$(-\infty, \infty)$$?

Accepted Answer

Cubic root function $$y = \sqrt[3]{x}$$

Question 20

For the piecewise function $$f(x) = \begin{cases} x^2$ & x \geq 0 \ -x-2 & x \u003c 0 \end{cases}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty) \cup (-\infty, -2)$$

Fundamental Functions and Piecewise Functions in Precalculus

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