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 function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 4

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

Accepted Answer

A graph with two branches, both above the x-axis, approaching infinity as $$x$$ approaches 0 from both sides.

Question 5

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

Accepted Answer

$$10$$

Question 6

Which function is NOT a polynomial?

Accepted Answer

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

Question 7

A chemical reaction rate is modeled by $$f(x) = x^2$. If the concentration doubles, by what factor does the reaction rate increase?

Accepted Answer

It quadruples.

Question 8

Which of the following describes the end behavior of $$f(x) = x^5$ as x$$ 	o -\infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 9

The function $$f(x) = \sqrt[3]{x} is $$defined for which values of $$x$$?

Accepted Answer

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

Question 10

A medical dosage is modeled by $$f(x) = |x|. If a $$patient receives a dose of $$-5 mg$$, what is the effective dosage?

Accepted Answer

$$5 mg$$

Question 11

Which of the following functions has a vertical asymptote at $$x=0$$?

Accepted Answer

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

Question 12

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

Accepted Answer

$$1$$

Question 13

Which function's graph is always increasing for all $$x in $$its domain?

Accepted Answer

$$f(x) = x$$

Question 14

If $$f(x) = x^4$, which of the following statements is true?

Accepted Answer

The graph is symmetric about the y-axis.

Question 15

Which function best models the depreciation of a car's value over time, assuming the value halves every year?

Accepted Answer

$$f(x) = 2$$^{-x}$$

Question 16

For the function $$f(x) = \frac{1}{x^3$}$$, what happens as $$x$$ approaches $$0$$ from the positive side?

Accepted Answer

$$f(x) 	o \infty$$

Question 17

Which of the following is the correct domain for $$f(x) = \sqrt[4]{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 18

A population grows according to $$f(x) = x^2$. If the initial population is 3$, what is the population after doubling the input?

Accepted Answer

$$36$$

Question 19

Which function is an example of a rational function?

Accepted Answer

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

Question 20

For the piecewise function $$f(x) = \begin{cases} 2x^2$ - 11 & x \leq -3 \ -2x^2$ + x & -3  -1 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$-9$$

Overview of Common Functions and Their Graphs in College Algebra

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