Q: Which of the following is the correct piecewise definition for the absolute value function $$f(x) = |x|$$?

$$f(x) = \begin{cases} x & x \geq 0 \\ -x & x \u003c 0 \end{cases}$$

Question 1

Which of the following best describes the domain and range of the squaring function $$f(x) = x^2$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 2

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

Accepted Answer

$$-1$$

Question 3

Which of the following statements is true about the graph of the absolute value function $$f(x) = |x|$$?

Accepted Answer

It is decreasing on $$(-\infty, 0)$$ and increasing on $$(0, \infty).$$

Question 4

A medical sensor measures the concentration of a drug in the bloodstream, modeled by $$f(x) = \sqrt{x}$$, where $$x is $$the time in hours since administration. What is the domain of this function in this context?

Accepted Answer

$$[0, \infty)$$

Question 5

Which function has a range of $$(-\infty, \infty)$$ and is increasing on its entire domain?

Accepted Answer

$$f(x) = x^3$

Question 6

For the piecewise function $$f(x) = \begin{cases} x-3 & x \leq 5 \ 2 & x \u003e 5 \end{cases}$$, what is $$f(7)$$?

Accepted Answer

$$2$$

Question 7

Which of the following best describes the range of the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

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

Question 8

A company’s profit is modeled by $$f(x) = |x-2|$$, where $$x is $$the number of products sold in thousands. What is the minimum profit, and for what value of $$x$$ does it occur?

Accepted Answer

Minimum profit is $$0 at$$ $$x=2$$

Question 9

Which of the following is the correct piecewise definition for the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$f(x) = \begin{cases} x & x \geq 0 \ -x & x \u003c 0 \end{cases}$$

Question 10

Given the function $$f(x) = 2x + 4$$ for $$x \u003c 1$$ and $$f(x) = 4 - x$$ for $$x \geq 1$$, what is $$f(1)$$?

Accepted Answer

$$3$$

Question 11

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$

Question 12

A chemical reaction’s rate is modeled by $$f(x) = x^2$. If the input doubles, how does the output change?

Accepted Answer

It quadruples.

Question 13

For the function $$f(x) = \sqrt{x}$$, which of the following is true?

Accepted Answer

The function is defined only for $$x \geq 0.$$

Question 14

Which of the following best describes the behavior of the function $$f(x) = x^2$?

Accepted Answer

Decreases on $$(-\infty, 0)$$ and increases on $$(0, \infty).$$

Question 15

Given the piecewise function $$f(x) = \begin{cases} -2x & x  2 \end{cases}$$, what is $$f(-5)$$?

Accepted Answer

$$10$$

Question 16

Which function’s graph passes through the points $$(-2, -2)$$, $$(0, 0)$$, and $$(2, 2)$$?

Accepted Answer

$$f(x) = x$$

Question 17

A temperature sensor outputs $$f(x) = |x-5|$$ where $$x is $$the measured temperature in $$^0C. $$What is the output when the temperature is $$2^0C$$?

Accepted Answer

$$3$$

Question 18

Which of the following is the correct graph for $$f(x) = \sqrt{x}$$?

Accepted Answer

Starts at $$(0,0)$$ and increases slowly to the right, only in the first quadrant.

Question 19

For the function $$f(x) = x^3$, which of the following is true?

Accepted Answer

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

Graphs of Basic Functions & Piecewise Functions: College Algebra Study Notes

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