Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 2

Given the function $$f(x) = x^3$, which statement about its graph is true?

Accepted Answer

It passes through the origin and is symmetric about the origin.

Question 3

What is the range of the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 4

Which of the following functions is NOT a polynomial function?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 5

For the rational function $$f(x) = \frac{1}{x^2$}$$, which of the following statements is true?

Accepted Answer

The graph is symmetric about the y-axis.

Question 6

A piecewise function is defined as $$f(x) = \begin{cases} 2x-1 & x  1 \end{cases}. $$What is $$f(2)$$?

Accepted Answer

$$1$$

Question 7

Which function has a graph that is always increasing for all $$x in $$its domain?

Accepted Answer

$$f(x) = x^3$

Question 8

The function $$f(x) = \frac{1}{x} is $$undefined at which value?

Accepted Answer

$$x = 0$$

Question 9

Which of the following best describes the end behavior of $$f(x) = x^4$ as x$$ 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 10

A student claims that the domain of $$f(x) = \sqrt[3]{x} is$$ $$[0, \infty). Is $$this correct?

Accepted Answer

No, because cube roots are defined for all real numbers.

Question 11

Which function has a graph with a sharp 'corner' at the origin?

Accepted Answer

$$f(x) = |x|$$

Question 12

Given the piecewise function $$f(x) = \begin{cases} 2x^2$ + 2 & x \u003c 3 \ x^2$ - 2 & x \geq 3 \end{cases}$$, what is $$f(4)$$?

Accepted Answer

$$14$$

Question 13

Which of the following is the correct range for $$f(x) = \frac{1}{x^2$}$$?

Accepted Answer

$$(0, \infty)$$

Question 14

Which function is an example of a rational function?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 15

A chemical reaction rate is modeled by $$f(x) = \frac{1}{x}$$, where $$x is $$the concentration of a reactant. What happens to the rate as $$x$$ approaches zero from the positive side?

Accepted Answer

The rate approaches infinity.

Question 16

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 17

If $$f(x) = x^5$, which of the following describes its symmetry?

Accepted Answer

Odd symmetry about the origin

Question 18

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

Accepted Answer

$$f(x) = x^3$

Question 19

A medical dosage is modeled by $$f(x) = |x|$$, where $$x is $$the deviation from the ideal dosage. What is the minimum value of $$f(x)$$?

Accepted Answer

$$0$$

Question 20

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

Accepted Answer

A graph that passes through the origin and is defined for all real $$x.$$

Overview of Common Functions and Their Graphs in College Algebra

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