Worksheets · Precalculus

Even and odd functions worksheet

Replace x with minus x and see what comes back. The same function means even, everything flipped in sign means odd, and anything else means neither.

Select your difficulty

Pick more than one for a sheet that mixes them.

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.

  1. Even, odd or neither? f(x)=−4x5+8x3
  2. Even, odd or neither? f(x)=−3x4−4x3−2
  3. Even, odd or neither? f(x)=−2x2−4x3
  4. Even, odd or neither? f(x)=2x3+4x5
  5. Even, odd or neither? f(x)=−3x2−2x4+6
  6. Even, odd or neither? f(x)=2x5+6x
  7. Even, odd or neither? f(x)=6∣x∣+8x3
  8. Even, odd or neither? f(x)=5x5−6x3
  9. Even, odd or neither? f(x)=−3x3−6x5
  10. Even, odd or neither? f(x)=−x4−8x−2
  11. Even, odd or neither? f(x)=−x4−6∣x∣+2
  12. Even, odd or neither? f(x)=−6x2+7x5−2
  13. Even, odd or neither? f(x)=x2−7x3+8
  14. Even, odd or neither? f(x)=2x+3x5
  15. Even, odd or neither? f(x)=−2x2−3x4+9
  16. Even, odd or neither? f(x)=3∣x∣−2x4+3
  17. Even, odd or neither? f(x)=−2x2+7x
  18. Even, odd or neither? f(x)=−3x4+6x2
  19. Even, odd or neither? f(x)=4x5−x3
  20. Even, odd or neither? f(x)=−4x5+x3

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Even and Odd FunctionsAnswer keyVersion 1

Date Period

Decide whether each function is even, odd or neither.

  1. Even, odd or neither? f(x)=−4x5+8x3Odd
  2. Even, odd or neither? f(x)=−3x4−4x3−2Neither
  3. Even, odd or neither? f(x)=−2x2−4x3Neither
  4. Even, odd or neither? f(x)=2x3+4x5Odd
  5. Even, odd or neither? f(x)=−3x2−2x4+6Even
  6. Even, odd or neither? f(x)=2x5+6xOdd
  7. Even, odd or neither? f(x)=6∣x∣+8x3Neither
  8. Even, odd or neither? f(x)=5x5−6x3Odd
  9. Even, odd or neither? f(x)=−3x3−6x5Odd
  10. Even, odd or neither? f(x)=−x4−8x−2Neither
  11. Even, odd or neither? f(x)=−x4−6∣x∣+2Even
  12. Even, odd or neither? f(x)=−6x2+7x5−2Neither
  13. Even, odd or neither? f(x)=x2−7x3+8Neither
  14. Even, odd or neither? f(x)=2x+3x5Odd
  15. Even, odd or neither? f(x)=−2x2−3x4+9Even
  16. Even, odd or neither? f(x)=3∣x∣−2x4+3Even
  17. Even, odd or neither? f(x)=−2x2+7xNeither
  18. Even, odd or neither? f(x)=−3x4+6x2Even
  19. Even, odd or neither? f(x)=4x5−x3Odd
  20. Even, odd or neither? f(x)=−4x5+x3Odd

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

f(x)=3x4−2x2

  1. Replace x with minus x.
  2. Both powers are even, so nothing changes sign.
  3. f of minus x is the same as f of x.

The answer is Even.

Where students go wrong

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.

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

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.

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 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.

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.