Worksheets · Precalculus

Function transformations worksheet

Replacing x with x minus h moves the graph h to the right, and adding k lifts it. Multiplying it out shows you what that actually does to the equation, which is the part a graph alone will not tell you.

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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

Transformations of Functions

Date Period

Write each transformed function in simplified form.

  1. If f(x)=−2x2, write f(x+4)+3
  2. If f(x)=−2x2−x−2, write f(x+4)−3
  3. If f(x)=−2x2−5x, write f(x−4)−4
  4. If f(x)=3x2−2x+2, write f(x+4)+1
  5. If f(x)=−2x2+6x, write f(x+2)+2
  6. If f(x)=3x2, write f(x+1)+5
  7. If f(x)=3x2+7x, write f(x+5)−4
  8. If f(x)=−x2+x, write f(x−5)−3
  9. If f(x)=x2−x+4, write f(x+2)+2
  10. If f(x)=2x2+2, write f(x−5)−6
  11. If f(x)=x2, write f(x+2)+5
  12. If f(x)=−x2+3x−4, write f(x−5)+2
  13. If f(x)=−x2−7, write f(x+2)−6
  14. If f(x)=−x2+3, write f(x−3)+2
  15. If f(x)=3x2−5x, write f(x−1)−2
  16. If f(x)=2x2+1, write f(x−3)+2
  17. If f(x)=x2+3x, write f(x−5)−6
  18. If f(x)=x2−7x−6, write f(x−1)+5
  19. If f(x)=2x2+5x+1, write f(x−1)−4
  20. If f(x)=−2x2−x, write f(x+4)+2

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

Sigma Prep · sigmaprep.io/worksheets

Name

Transformations of FunctionsAnswer keyVersion 1

Date Period

Write each transformed function in simplified form.

  1. If f(x)=−2x2, write f(x+4)+3−2x2−16x−29
  2. If f(x)=−2x2−x−2, write f(x+4)−3−2x2−17x−41
  3. If f(x)=−2x2−5x, write f(x−4)−4−2x2+11x−16
  4. If f(x)=3x2−2x+2, write f(x+4)+13x2+22x+43
  5. If f(x)=−2x2+6x, write f(x+2)+2−2x2−2x+6
  6. If f(x)=3x2, write f(x+1)+53x2+6x+8
  7. If f(x)=3x2+7x, write f(x+5)−43x2+37x+106
  8. If f(x)=−x2+x, write f(x−5)−3−x2+11x−33
  9. If f(x)=x2−x+4, write f(x+2)+2x2+3x+8
  10. If f(x)=2x2+2, write f(x−5)−62x2−20x+46
  11. If f(x)=x2, write f(x+2)+5x2+4x+9
  12. If f(x)=−x2+3x−4, write f(x−5)+2−x2+13x−42
  13. If f(x)=−x2−7, write f(x+2)−6−x2−4x−17
  14. If f(x)=−x2+3, write f(x−3)+2−x2+6x−4
  15. If f(x)=3x2−5x, write f(x−1)−23x2−11x+6
  16. If f(x)=2x2+1, write f(x−3)+22x2−12x+21
  17. If f(x)=x2+3x, write f(x−5)−6x2−7x+4
  18. If f(x)=x2−7x−6, write f(x−1)+5x2−9x+7
  19. If f(x)=2x2+5x+1, write f(x−1)−42x2+x−6
  20. If f(x)=−2x2−x, write f(x+4)+2−2x2−17x−34

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

How to do these

If f(x)=x2+4x, write f(x−3)+1

  1. Put x minus 3 in wherever x was.
  2. That gives (x - 3) squared plus 4(x - 3).
  3. Expand and add the 1.

The answer is x2−2x−2.

Where students go wrong

Moving the graph the way the sign looks. f(x - 3) shifts it three to the RIGHT, not left: the parenthesis has to reach zero later, so every x has to be bigger.

Also called shifting functions, translating graphs, f(x - h) + k or horizontal and vertical shifts.

Questions about these worksheets

Yes. Every function transformations 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 function transformations 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 two 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.

Moving the graph the way the sign looks. f(x - 3) shifts it three to the RIGHT, not left: the parenthesis has to reach zero later, so every x has to be bigger.