Q: Which of the following is a piecewise-defined function?

$$f(x) = \begin{cases} 2x+3 & x \leq 0 \\ -x^2$+3 & x \u003e 0 \end{cases}$$

Question 1

Which of the following functions is NOT continuous over its entire domain?

Accepted Answer

$$f(x) = \lfloor x \rfloor ($$the greatest integer function)

Question 2

What is the domain of the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 3

A package delivery company charges $$25 for up to 2 pounds, and 3 $$for each additional pound or fraction thereof. Which function best models the cost $$C(x)$$ for $$x$$ pounds?

Accepted Answer

$$C(x) = 25 + 3\lceil x-2 \rceil$$ for $$x \u003e 2$$

Question 4

Which of the following statements about the function $$f(x) = x^2$ is TRUE?

Accepted Answer

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

Question 5

Which function is defined for all real numbers and is always increasing?

Accepted Answer

$$f(x) = x^3$

Question 6

Which of the following is a piecewise-defined function?

Accepted Answer

$$f(x) = \begin{cases} 2x+3 & x \leq 0 \ -x^2$+3 & x \u003e 0 \end{cases}$$

Question 7

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 8

For the greatest integer function $$f(x) = \lfloor x \rfloor$$, what is $$f(2.7)$$?

Accepted Answer

$$2$$

Question 9

Which function has a point of discontinuity at $$x = 3$$?

Accepted Answer

$$f(x) = \frac{x-3}{x-3}$$

Question 10

Which of the following best describes the range of the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 11

A medical device records the cube root of a patient's blood pressure reading. If the reading is 64, what value does the device display?

Accepted Answer

$$4$$

Question 12

Which function is constant on intervals between integers and has jump discontinuities at integer values?

Accepted Answer

$$f(x) = \lfloor x \rfloor$$

Question 13

For the piecewise function $$f(x) = \begin{cases} -2x+5 & x \leq 2 \ x+1 & x \u003e 2 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$1$$

Question 14

Which of the following functions is increasing on its entire domain?

Accepted Answer

$$f(x) = x^3$

Question 15

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

Accepted Answer

$$[0, \infty)$$

Question 16

Which function pairs every real number $$x$$ with the greatest integer less than or equal to $$x$$?

Accepted Answer

$$f(x) = \lfloor x \rfloor$$

Question 17

Which of the following is the correct domain for the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

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

Question 18

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

Accepted Answer

It quadruples.

Question 19

Which of the following is TRUE about the relation $$x = y^2$?

Accepted Answer

It is not a function because a single $$x$$ value can correspond to two $$y$$ values.

Graphs of Basic Functions and Their Properties

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