Give the domain, range and end behavior of f(x) = 3x^6

Domain (-infinity, infinity); range [0, infinity); f(x) to infinity as x to

Give the domain, range and end behavior of f(x) = x^3

Domain (-infinity, infinity); range (-infinity, infinity); f(x) to infinity as x to infinity, f(x) to -infinity as x to -infinity

Give the domain, range and end behavior of f(x) = -5x^6

Domain (-infinity, infinity); range (-infinity, 0]; f(x) to -infinity as x to

Give the domain, range and end behavior of f(x) = -x^5

Domain (-infinity, infinity); range (-infinity, infinity); f(x) to -infinity as x to infinity, f(x) to infinity as x to -infinity

Give the domain, range and end behavior of f(x) = -3x^4

Domain (-infinity, infinity); range (-infinity, 0]; f(x) to -infinity as x to

Write as kx^p and give the power and the constant: f(x) = 6[4]x^3

f(x) = 6x^3/4; power 3/4, constant 6

Give the domain and range of f(x) = 3x^-1/2

Domain (0, infinity); range (0, infinity)

For the graph of f(x) = 3x^2, give the intercepts, where it is continuous, and where it increases and decreases.

Intercept (0, 0); continuous on (-infinity, infinity); increasing on (0, infinity); decreasing on (-infinity, 0)

Worksheets · Precalculus

Power functions worksheet

A power function is a constant times x raised to a fixed power, f(x) = kx^p. The power can be negative or a fraction, so 5/x^2 and 3 times the square root of x both count. What does not count is anything with a second term, or with x in the exponent.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Power Functions Date Period Answer each question. Decide if it is a power function Is $f (x) = x^{4} + 9$ a power function? If so, give its power and constant. Is $f (x) = 5 \sqrt[3]{x}$ a power function? If so, give its power and constant. Is $f (x) = 8^{x}$ a power function? If so, give its power and constant. Is $f (x) = {(x + 2)}^{3}$ a power function? If so, give its power and constant. Is $f (x) = \frac{4}{x^{2}}$ a power function? If so, give its power and constant. Find the power function through two points Write the power function $y = k x^{p}$ through $(1, - 3)$ and $(3, - 81)$ Write the power function $y = k x^{p}$ through $(2, 6)$ and $(6, 2)$ Write the power function $y = k x^{p}$ through $(1, - 8)$ and $(2, - 32)$ Write the power function $y = k x^{p}$ through $(3, 25)$ and $(5, 9)$ Write the power function $y = k x^{p}$ through $(1, - 10)$ and $(2, - 5)$ Classify as even, odd or neither Is $f (x) = - 8 x^{3}$ even, odd, or neither? Is $f (x) = - \frac{9}{x^{4}}$ even, odd, or neither? Is $f (x) = \frac{2}{x^{4}}$ even, odd, or neither? Is $f (x) = 7 x^{3}$ even, odd, or neither? Is $f (x) = - \frac{2}{x}$ even, odd, or neither? Give the domain, range and end behavior Give the domain, range and end behavior of $f (x) = 3 x^{6}$ Give the domain, range and end behavior of $f (x) = x^{3}$ Give the domain, range and end behavior of $f (x) = - 5 x^{6}$ Give the domain, range and end behavior of $f (x) = - x^{5}$ Give the domain, range and end behavior of $f (x) = - 3 x^{4}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Power Functions

Date Period

Answer each question.

Decide if it is a power function
Is $f (x) = x^{4} + 9$ a power function? If so, give its power and constant.
Is $f (x) = 5 \sqrt[3]{x}$ a power function? If so, give its power and constant.
Is $f (x) = 8^{x}$ a power function? If so, give its power and constant.
Is $f (x) = {(x + 2)}^{3}$ a power function? If so, give its power and constant.
Is $f (x) = \frac{4}{x^{2}}$ a power function? If so, give its power and constant.

Find the power function through two points
Write the power function $y = k x^{p}$ through $(1, - 3)$ and $(3, - 81)$
Write the power function $y = k x^{p}$ through $(2, 6)$ and $(6, 2)$
Write the power function $y = k x^{p}$ through $(1, - 8)$ and $(2, - 32)$
Write the power function $y = k x^{p}$ through $(3, 25)$ and $(5, 9)$
Write the power function $y = k x^{p}$ through $(1, - 10)$ and $(2, - 5)$

Classify as even, odd or neither
Is $f (x) = - 8 x^{3}$ even, odd, or neither?
Is $f (x) = - \frac{9}{x^{4}}$ even, odd, or neither?
Is $f (x) = \frac{2}{x^{4}}$ even, odd, or neither?
Is $f (x) = 7 x^{3}$ even, odd, or neither?
Is $f (x) = - \frac{2}{x}$ even, odd, or neither?

Give the domain, range and end behavior
Give the domain, range and end behavior of $f (x) = 3 x^{6}$
Give the domain, range and end behavior of $f (x) = x^{3}$
Give the domain, range and end behavior of $f (x) = - 5 x^{6}$
Give the domain, range and end behavior of $f (x) = - x^{5}$
Give the domain, range and end behavior of $f (x) = - 3 x^{4}$



Sigma Prep · sigmaprep.io/worksheets Name Power FunctionsAnswer keyVersion 1 Date Period Answer each question. Decide if it is a power function Is $f (x) = x^{4} + 9$ a power function? If so, give its power and constant.No Is $f (x) = 5 \sqrt[3]{x}$ a power function? If so, give its power and constant.Yes; power $\frac{1}{3}$ , constant $5$ Is $f (x) = 8^{x}$ a power function? If so, give its power and constant.No Is $f (x) = {(x + 2)}^{3}$ a power function? If so, give its power and constant.No Is $f (x) = \frac{4}{x^{2}}$ a power function? If so, give its power and constant.Yes; power $- 2$ , constant $4$ Find the power function through two points Write the power function $y = k x^{p}$ through $(1, - 3)$ and $(3, - 81)$ $y = - 3 x^{3}$ Write the power function $y = k x^{p}$ through $(2, 6)$ and $(6, 2)$ $y = \frac{12}{x}$ Write the power function $y = k x^{p}$ through $(1, - 8)$ and $(2, - 32)$ $y = - 8 x^{2}$ Write the power function $y = k x^{p}$ through $(3, 25)$ and $(5, 9)$ $y = \frac{225}{x^{2}}$ Write the power function $y = k x^{p}$ through $(1, - 10)$ and $(2, - 5)$ $y = - \frac{10}{x}$ Classify as even, odd or neither Is $f (x) = - 8 x^{3}$ even, odd, or neither?Odd Is $f (x) = - \frac{9}{x^{4}}$ even, odd, or neither?Even Is $f (x) = \frac{2}{x^{4}}$ even, odd, or neither?Even Is $f (x) = 7 x^{3}$ even, odd, or neither?Odd Is $f (x) = - \frac{2}{x}$ even, odd, or neither?Odd Give the domain, range and end behavior Give the domain, range and end behavior of $f (x) = 3 x^{6}$ Domain $(- \infty, \infty)$ ; range $[0, \infty)$ ; $f (x) \to \infty$ as $x \to \pm \infty$ Give the domain, range and end behavior of $f (x) = x^{3}$ Domain $(- \infty, \infty)$ ; range $(- \infty, \infty)$ ; $f (x) \to \infty$ as $x \to \infty$ , $f (x) \to - \infty$ as $x \to - \infty$ Give the domain, range and end behavior of $f (x) = - 5 x^{6}$ Domain $(- \infty, \infty)$ ; range $(- \infty, 0]$ ; $f (x) \to - \infty$ as $x \to \pm \infty$ Give the domain, range and end behavior of $f (x) = - x^{5}$ Domain $(- \infty, \infty)$ ; range $(- \infty, \infty)$ ; $f (x) \to - \infty$ as $x \to \infty$ , $f (x) \to \infty$ as $x \to - \infty$ Give the domain, range and end behavior of $f (x) = - 3 x^{4}$ Domain $(- \infty, \infty)$ ; range $(- \infty, 0]$ ; $f (x) \to - \infty$ as $x \to \pm \infty$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Power FunctionsAnswer keyVersion 1

Date Period

Answer each question.

Decide if it is a power function
Is $f (x) = x^{4} + 9$ a power function? If so, give its power and constant.No
Is $f (x) = 5 \sqrt[3]{x}$ a power function? If so, give its power and constant.Yes; power $\frac{1}{3}$ , constant $5$
Is $f (x) = 8^{x}$ a power function? If so, give its power and constant.No
Is $f (x) = {(x + 2)}^{3}$ a power function? If so, give its power and constant.No
Is $f (x) = \frac{4}{x^{2}}$ a power function? If so, give its power and constant.Yes; power $- 2$ , constant $4$

Find the power function through two points
Write the power function $y = k x^{p}$ through $(1, - 3)$ and $(3, - 81)$ $y = - 3 x^{3}$
Write the power function $y = k x^{p}$ through $(2, 6)$ and $(6, 2)$ $y = \frac{12}{x}$
Write the power function $y = k x^{p}$ through $(1, - 8)$ and $(2, - 32)$ $y = - 8 x^{2}$
Write the power function $y = k x^{p}$ through $(3, 25)$ and $(5, 9)$ $y = \frac{225}{x^{2}}$
Write the power function $y = k x^{p}$ through $(1, - 10)$ and $(2, - 5)$ $y = - \frac{10}{x}$

Classify as even, odd or neither
Is $f (x) = - 8 x^{3}$ even, odd, or neither?Odd
Is $f (x) = - \frac{9}{x^{4}}$ even, odd, or neither?Even
Is $f (x) = \frac{2}{x^{4}}$ even, odd, or neither?Even
Is $f (x) = 7 x^{3}$ even, odd, or neither?Odd
Is $f (x) = - \frac{2}{x}$ even, odd, or neither?Odd

Give the domain, range and end behavior
Give the domain, range and end behavior of $f (x) = 3 x^{6}$ Domain $(- \infty, \infty)$ ; range $[0, \infty)$ ; $f (x) \to \infty$ as $x \to \pm \infty$
Give the domain, range and end behavior of $f (x) = x^{3}$ Domain $(- \infty, \infty)$ ; range $(- \infty, \infty)$ ; $f (x) \to \infty$ as $x \to \infty$ , $f (x) \to - \infty$ as $x \to - \infty$
Give the domain, range and end behavior of $f (x) = - 5 x^{6}$ Domain $(- \infty, \infty)$ ; range $(- \infty, 0]$ ; $f (x) \to - \infty$ as $x \to \pm \infty$
Give the domain, range and end behavior of $f (x) = - x^{5}$ Domain $(- \infty, \infty)$ ; range $(- \infty, \infty)$ ; $f (x) \to - \infty$ as $x \to \infty$ , $f (x) \to \infty$ as $x \to - \infty$
Give the domain, range and end behavior of $f (x) = - 3 x^{4}$ Domain $(- \infty, \infty)$ ; range $(- \infty, 0]$ ; $f (x) \to - \infty$ as $x \to \pm \infty$

How to do these

Write the power function $y = k x^{p}$ through $(2, 24)$ and $(4, 192)$

Divide the two: 192 / 24 = 8 and 4 / 2 = 2, so 2 to the p is 8 and p = 3.
Then 24 = k times 2 cubed, so k = 3.

The answer is $y = 3 x^{3}$ .

Where students go wrong

Calling 2^x a power function because it has a power in it. In a power function the base is x and the exponent is fixed; in 2^x it is the other way round, and that is an exponential function.

Also called power function, constant of variation, power and constant or even and odd power functions.

What you can put on this worksheet

Is it a power function: Is $f (x) = 7 x^{2}$ a power function? If so, give its power and constant. → Yes; power $2$ , constant $7$
The power function through two points: Write the power function $y = k x^{p}$ through $(1, 4)$ and $(3, 108)$ → $y = 4 x^{3}$
Even, odd or neither: Is $f (x) = 6 x^{2}$ even, odd, or neither? → Even
Domain, range and end behavior: Give the domain, range and end behavior of $f (x) = 3 x^{6}$ → Domain $(- \infty, \infty)$ ; range $[0, \infty)$ ; $f (x) \to \infty$ as $x \to \pm \infty$
Roots and fractions to kx^p: Write as $k x^{p}$ and give the power and the constant: $f (x) = 6 \sqrt[4]{x^{3}}$ → $f (x) = 6 x^{\frac{3}{4}}$ ; power $\frac{3}{4}$ , constant $6$
Negative and fractional powers: domain and range: Give the domain and range of $f (x) = 3 x^{- \frac{1}{2}}$ → Domain $(0, \infty)$ ; range $(0, \infty)$
Intercepts, continuity, increasing and decreasing: For the graph of $f (x) = 3 x^{2}$ , give the intercepts, where it is continuous, and where it increases and decreases. → Intercept $(0, 0)$ ; continuous on $(- \infty, \infty)$ ; increasing on $(0, \infty)$ ; decreasing on $(- \infty, 0)$

Questions about these worksheets

Yes. Every power functions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the power functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 7: is it a power function, the power function through two points, even, odd or neither, domain, range and end behavior, roots and fractions to kx^p, negative and fractional powers: domain and range and intercepts, continuity, increasing and decreasing. Tick as many as you want and set how many of each, or let it spread them evenly.

Calling 2^x a power function because it has a power in it. In a power function the base is x and the exponent is fixed; in 2^x it is the other way round, and that is an exponential function.

Power functions worksheet

Select your difficulty

Decide if it is a power function

Find the power function through two points

Classify as even, odd or neither

Give the domain, range and end behavior

Decide if it is a power function

Find the power function through two points

Classify as even, odd or neither

Give the domain, range and end behavior

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these power functions worksheets free?+

Do the power functions worksheets come with an answer key?+

Are these power functions worksheets printable?+

What grade are these power functions worksheets for?+

Can I get a different version of the same power functions worksheet?+

Is this a free alternative to Kuta Software for power functions?+

Can I choose how hard the power functions questions are?+

What kinds of question are on a power functions worksheet?+

What do students get wrong with power functions?+