Even and odd functions worksheet for Algebra 2

Algebra 2 uses even and odd as a quick description of a graph's symmetry: even functions mirror across the y-axis and odd ones look the same after a half turn about the origin. You test formulas, read tables of values, and check equations for x-axis, y-axis and origin symmetry.

Also taught in Precalculus, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Even and Odd Functions Date Period Decide whether each function is even, odd or neither, or test each equation for symmetry. Classify as even, odd or neither Even, odd or neither? $f (x) = - 2 x^{2} + 8 x + 5$ Even, odd or neither? $f (x) = ∣ x ∣ + x$ Even, odd or neither? $f (x) = - 3 x^{2} - x$ Even, odd or neither? $f (x) = \frac{∣ x ∣ - 1}{x^{2} + 2}$ Even, odd or neither? $f (x) = - 3 x^{4} - 8 x$ Even, odd or neither? $f (x) = \frac{x^{5}}{x^{2} + 8}$ Even, odd or neither? $f (x) = 2 x - 6 x^{3}$ Even, odd or neither? $f (x) = x^{2} + x ∣ x ∣$ Even, odd or neither? $f (x) = - 2 x^{2} + 5 x^{4} + 1$ Even, odd or neither? $f (x) = \frac{x ∣ x ∣}{x^{2} + 9}$ Classify from a table as even, odd or neither $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 8 & - 4 & - 4 & - 4 & 6 \end{array} \end{aligned}$ $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 5 & 1 & - 3 & 1 & 5 \end{array} \end{aligned}$ $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 7 & 6 & 0 & - 6 & 7 \end{array} \end{aligned}$ $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 2 & - 6 & 3 & - 6 & - 2 \end{array} \end{aligned}$ $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 6 & - 3 & 0 & 3 & 6 \end{array} \end{aligned}$ Test an equation for symmetry Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x = 2 y^{2} + 1$ Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y^{2} = x^{3}$ Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x^{2} + y^{2} = 64$ Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y = - 3 x^{3} + 3 x$ Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $5 x^{2} + 3 y^{2} = 3$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Even and Odd Functions

Date Period

Decide whether each function is even, odd or neither, or test each equation for symmetry.

Classify as even, odd or neither
Even, odd or neither? $f (x) = - 2 x^{2} + 8 x + 5$
Even, odd or neither? $f (x) = ∣ x ∣ + x$
Even, odd or neither? $f (x) = - 3 x^{2} - x$
Even, odd or neither? $f (x) = \frac{∣ x ∣ - 1}{x^{2} + 2}$
Even, odd or neither? $f (x) = - 3 x^{4} - 8 x$
Even, odd or neither? $f (x) = \frac{x^{5}}{x^{2} + 8}$
Even, odd or neither? $f (x) = 2 x - 6 x^{3}$
Even, odd or neither? $f (x) = x^{2} + x ∣ x ∣$
Even, odd or neither? $f (x) = - 2 x^{2} + 5 x^{4} + 1$
Even, odd or neither? $f (x) = \frac{x ∣ x ∣}{x^{2} + 9}$

Classify from a table as even, odd or neither
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 8 & - 4 & - 4 & - 4 & 6 \end{array} \end{aligned}$
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 5 & 1 & - 3 & 1 & 5 \end{array} \end{aligned}$
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 7 & 6 & 0 & - 6 & 7 \end{array} \end{aligned}$
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 2 & - 6 & 3 & - 6 & - 2 \end{array} \end{aligned}$
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 6 & - 3 & 0 & 3 & 6 \end{array} \end{aligned}$

Test an equation for symmetry
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x = 2 y^{2} + 1$
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y^{2} = x^{3}$
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x^{2} + y^{2} = 64$
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y = - 3 x^{3} + 3 x$
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $5 x^{2} + 3 y^{2} = 3$



Sigma Prep · sigmaprep.io/worksheets Name Even and Odd FunctionsAnswer keyVersion 2 Date Period Decide whether each function is even, odd or neither, or test each equation for symmetry. Classify as even, odd or neither Even, odd or neither? $f (x) = - 2 x^{2} + 8 x + 5$ Neither Even, odd or neither? $f (x) = ∣ x ∣ + x$ Neither Even, odd or neither? $f (x) = - 3 x^{2} - x$ Neither Even, odd or neither? $f (x) = \frac{∣ x ∣ - 1}{x^{2} + 2}$ Even Even, odd or neither? $f (x) = - 3 x^{4} - 8 x$ Neither Even, odd or neither? $f (x) = \frac{x^{5}}{x^{2} + 8}$ Odd Even, odd or neither? $f (x) = 2 x - 6 x^{3}$ Odd Even, odd or neither? $f (x) = x^{2} + x ∣ x ∣$ Neither Even, odd or neither? $f (x) = - 2 x^{2} + 5 x^{4} + 1$ Even Even, odd or neither? $f (x) = \frac{x ∣ x ∣}{x^{2} + 9}$ Odd Classify from a table as even, odd or neither $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 8 & - 4 & - 4 & - 4 & 6 \end{array} \end{aligned}$ Neither $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 5 & 1 & - 3 & 1 & 5 \end{array} \end{aligned}$ Even $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 7 & 6 & 0 & - 6 & 7 \end{array} \end{aligned}$ Odd $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 2 & - 6 & 3 & - 6 & - 2 \end{array} \end{aligned}$ Even $\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 6 & - 3 & 0 & 3 & 6 \end{array} \end{aligned}$ Odd Test an equation for symmetry Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x = 2 y^{2} + 1$ $x$ -axis only Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y^{2} = x^{3}$ $x$ -axis only Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x^{2} + y^{2} = 64$ $x$ -axis, $y$ -axis and origin Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y = - 3 x^{3} + 3 x$ Origin only Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $5 x^{2} + 3 y^{2} = 3$ $x$ -axis, $y$ -axis and origin Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Even and Odd FunctionsAnswer keyVersion 2

Date Period

Decide whether each function is even, odd or neither, or test each equation for symmetry.

Classify as even, odd or neither
Even, odd or neither? $f (x) = - 2 x^{2} + 8 x + 5$ Neither
Even, odd or neither? $f (x) = ∣ x ∣ + x$ Neither
Even, odd or neither? $f (x) = - 3 x^{2} - x$ Neither
Even, odd or neither? $f (x) = \frac{∣ x ∣ - 1}{x^{2} + 2}$ Even
Even, odd or neither? $f (x) = - 3 x^{4} - 8 x$ Neither
Even, odd or neither? $f (x) = \frac{x^{5}}{x^{2} + 8}$ Odd
Even, odd or neither? $f (x) = 2 x - 6 x^{3}$ Odd
Even, odd or neither? $f (x) = x^{2} + x ∣ x ∣$ Neither
Even, odd or neither? $f (x) = - 2 x^{2} + 5 x^{4} + 1$ Even
Even, odd or neither? $f (x) = \frac{x ∣ x ∣}{x^{2} + 9}$ Odd

Classify from a table as even, odd or neither
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 8 & - 4 & - 4 & - 4 & 6 \end{array} \end{aligned}$ Neither
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 5 & 1 & - 3 & 1 & 5 \end{array} \end{aligned}$ Even
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 7 & 6 & 0 & - 6 & 7 \end{array} \end{aligned}$ Odd
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 2 & - 6 & 3 & - 6 & - 2 \end{array} \end{aligned}$ Even
$\begin{aligned} Is the function even, odd or neither? \\ \begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & - 6 & - 3 & 0 & 3 & 6 \end{array} \end{aligned}$ Odd

Test an equation for symmetry
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x = 2 y^{2} + 1$ $x$ -axis only
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y^{2} = x^{3}$ $x$ -axis only
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $x^{2} + y^{2} = 64$ $x$ -axis, $y$ -axis and origin
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y = - 3 x^{3} + 3 x$ Origin only
Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $5 x^{2} + 3 y^{2} = 3$ $x$ -axis, $y$ -axis and origin

How to do these

Even, odd or neither? $f (x) = x^{3} - x + 1$

f(-x) = -x³ + x + 1.
That is not f(x), since the x terms changed sign.
It is not -f(x) either, since the 1 did not change sign.

The answer is Neither.

Where students go wrong

Deciding from the exponents alone and ignoring the constant. A constant counts as an even term, so x³ - x + 1 is neither, not odd.

Also called even or odd functions, symmetry of functions or function symmetry.

What you can put on this worksheet

Even, odd or neither: Even, odd or neither? $f (x) = 5 x - 4 x^{3}$ → Odd
From a table: Is the function even, odd or neither?
$\begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & 5 & - 7 & 0 & 7 & - 5 \end{array}$ → Odd
Rational and radical formulas: Even, odd or neither? $f (x) = \frac{∣ x ∣ - 6}{x^{2} + 7}$ → Even
Symmetry of an equation: Test for symmetry about the $x$ -axis, the $y$ -axis and the origin: $y = ∣ x ∣ + 1$ → $y$ -axis only

Questions about these worksheets

Yes. Every even and odd 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.

Algebra 2 is usually taken around 10th or 11th 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 even and odd 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 4: even, odd or neither, from a table, rational and radical formulas and symmetry of an equation. Tick as many as you want and set how many of each, or let it spread them evenly.

Assuming a function has to be one or the other. Most are neither, and a single odd term mixed in with even ones is enough to spoil both.

Even and odd functions worksheet for Algebra 2

Select your difficulty

Classify as even, odd or neither

Classify from a table as even, odd or neither

Test an equation for symmetry

Classify as even, odd or neither

Classify from a table as even, odd or neither

Test an equation for symmetry

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these even and odd functions worksheets free?+

Do the even and odd functions worksheets come with an answer key?+

Are these even and odd functions worksheets printable?+

What grade are these even and odd functions worksheets for?+

Can I get a different version of the same even and odd functions worksheet?+

Is this a free alternative to Kuta Software for even and odd functions?+

Can I choose how hard the even and odd functions questions are?+

What kinds of question are on a even and odd functions worksheet?+

What do students get wrong with even and odd functions?+