Worksheets · Algebra 2

Parent functions and transformations worksheet

Six shapes cover most of the course: a line, a parabola, a cubic, an absolute value, a square root and a reciprocal. Everything else is one of those six moved about. Learn where each one sits and the rest is reading a, h and k off the equation.

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

Parent Functions and Transformations

Date Period

Graph each function, or describe the transformation.

  1. Graph y=∣x−4∣+4-10-10-5-55510100
  2. Describe the transformation from y=x2 to y=−(x+1)2+4
  3. Graph y=−(x+1)3−2-10-10-5-55510100
  4. Describe the transformation from y=x to y=−x−1
  5. Graph y=∣x+4∣−1-10-10-5-55510100
  6. Describe the transformation from y=x3 to y=2(x+3)3+1
  7. Graph y=2(x−2)3-10-10-5-55510100
  8. Describe the transformation from y=∣x∣ to y=2∣x−2∣−3
  9. Graph y=−(x+3)2+2-10-10-5-55510100
  10. Describe the transformation from y=x3 to y=(x+4)3+1
  11. Graph y=x−2−1-10-10-5-55510100
  12. Describe the transformation from y=x2 to y=2(x−4)2+2
  13. Graph y=2x+3−4-10-10-5-55510100
  14. Describe the transformation from y=x to y=x+4
  15. Graph y=∣x−4∣−3-10-10-5-55510100
  16. Describe the transformation from y=x to y=x+3−1
  17. Graph y=−(x)2−4-10-10-5-55510100
  18. Describe the transformation from y=x to y=2x+3−2
  19. Graph y=x−1-10-10-5-55510100
  20. Describe the transformation from y=x2 to y=(x+4)2−2

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

Sigma Prep · sigmaprep.io/worksheets

Name

Parent Functions and TransformationsAnswer keyVersion 1

Date Period

Graph each function, or describe the transformation.

  1. Graph y=∣x−4∣+4-10-10-5-55510100Anchor at (4,4)
  2. Describe the transformation from y=x2 to y=−(x+1)2+4reflected in the x-axis, left 1, up 4
  3. Graph y=−(x+1)3−2-10-10-5-55510100Anchor at (−1,−2)
  4. Describe the transformation from y=x to y=−x−1reflected in the x-axis, down 1
  5. Graph y=∣x+4∣−1-10-10-5-55510100Anchor at (−4,−1)
  6. Describe the transformation from y=x3 to y=2(x+3)3+1stretched by 2, left 3, up 1
  7. Graph y=2(x−2)3-10-10-5-55510100Anchor at (2,0)
  8. Describe the transformation from y=∣x∣ to y=2∣x−2∣−3stretched by 2, right 2, down 3
  9. Graph y=−(x+3)2+2-10-10-5-55510100Anchor at (−3,2)
  10. Describe the transformation from y=x3 to y=(x+4)3+1left 4, up 1
  11. Graph y=x−2−1-10-10-5-55510100Anchor at (2,−1)
  12. Describe the transformation from y=x2 to y=2(x−4)2+2stretched by 2, right 4, up 2
  13. Graph y=2x+3−4-10-10-5-55510100Anchor at (−3,−4)
  14. Describe the transformation from y=x to y=x+4up 4
  15. Graph y=∣x−4∣−3-10-10-5-55510100Anchor at (4,−3)
  16. Describe the transformation from y=x to y=x+3−1left 3, down 1
  17. Graph y=−(x)2−4-10-10-5-55510100Anchor at (0,−4)
  18. Describe the transformation from y=x to y=2x+3−2stretched by 2, left 3, down 2
  19. Graph y=x−1-10-10-5-55510100Anchor at (1,0)
  20. Describe the transformation from y=x2 to y=(x+4)2−2left 4, down 2

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

How to do these

Graph y=−2∣x−3∣+1

  1. The parent is y = |x|, the V with its corner at the origin.
  2. x - 3 moves it right 3, and + 1 moves it up 1, so the corner is at (3, 1).
  3. The -2 flips it upside down and makes it twice as steep.

The answer is Anchor at (3,1).

Where students go wrong

Reading the horizontal shift backwards. x - 3 moves the graph right, not left, because 3 is the value that makes the bracket zero. The other slip is applying the stretch to the shift: in a f(x - h) + k the a multiplies the height only, so the corner stays where h and k put it.

Also called transformations of functions, parent graphs, shifting and stretching graphs or translations of functions.

What you can put on this worksheet

Graph the transformation
Graph y=(x+3)3 → Anchor at (−3,0)
Describe the transformation
Describe the transformation from y=x3 to y=(x+3)3 → left 3
Write the equation from the description
Write the equation: y=x3 left 3 → y=(x+3)3

Questions about these worksheets

Yes. Every parent functions and 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.

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 parent functions and 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 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 3: graph the transformation, describe the transformation and write the equation from the description. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading the horizontal shift backwards. x - 3 moves the graph right, not left, because 3 is the value that makes the bracket zero. The other slip is applying the stretch to the shift: in a f(x - h) + k the a multiplies the height only, so the corner stays where h and k put it.