Worksheets · Algebra 2

Parent functions and transformations worksheet for Algebra 2

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.

Also taught in Algebra 1 and Precalculus, each at its own level and with its own examples.

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.

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 answer as asked.

  1. Graph the transformed function

    Graph y=∣x−4∣+4−10−10−5−5551010
  2. Graph y=−(x+2)2−3−10−10−5−5551010
  3. Graph y=2(x+2)3+2−10−10−5−5551010
  4. Graph y=2x+3+1−10−10−5−5551010
  5. Graph y=2x−2+2−10−10−5−5551010

  1. Describe the transformation

    Describe the transformation from y=x2 to y=−(x+1)2+4 using vertical stretches, reflections and shifts.
  2. Describe the transformation from y=x to y=−x+3 using vertical stretches, reflections and vertical shifts.
  3. Describe the transformation from y=x to y=x−2 using vertical stretches, reflections and vertical shifts.
  4. Describe the transformation from y=∣x∣ to y=∣x+1∣+3 using vertical stretches, reflections and shifts.
  5. Describe the transformation from y=∣x∣ to y=∣x+1∣−2 using vertical stretches, reflections and shifts.

  1. Describe horizontal stretches and reflections

    Describe the transformation from y=x3 to y=(12x)3 as a horizontal stretch or shrink
  2. Describe the transformation from y=x2 to y=(3x)2 as a horizontal stretch or shrink
  3. Describe the transformation from y=x to y=−x
  4. Describe the transformation from y=∣x∣ to y=∣13x∣ as a horizontal stretch or shrink
  5. Describe the transformation from y=x2 to y=(14x)2 as a horizontal stretch or shrink

  1. Name the parent function

    Name the parent function of
    y=− ⁣∣x−3∣
  2. Name the parent function of
    y=3x−3+2
  3. Name the parent function of
    y=−1x−2
  4. Name the parent function of
    y=2x+13+4
  5. Name the parent function of
    y=−(x−4)3−5

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 answer as asked.

  1. Graph the transformed function

    Graph y=∣x−4∣+4−10−10−5−5551010Vertex (4,4)
  2. Graph y=−(x+2)2−3−10−10−5551010−5Vertex (−2,−3)
  3. Graph y=2(x+2)3+2−10−10−5−5510510Center (−2,2)
  4. Graph y=2x+3+1−10−10−5−5551010Starts at (−3,1)
  5. Graph y=2x−2+2−10−10−5−5551010Starts at (2,2)

  1. Describe the transformation

    Describe the transformation from y=x2 to y=−(x+1)2+4 using vertical stretches, reflections and shifts.reflection in the x-axis, left 1, up 4
  2. Describe the transformation from y=x to y=−x+3 using vertical stretches, reflections and vertical shifts.reflection in the x-axis, up 3
  3. Describe the transformation from y=x to y=x−2 using vertical stretches, reflections and vertical shifts.down 2
  4. Describe the transformation from y=∣x∣ to y=∣x+1∣+3 using vertical stretches, reflections and shifts.left 1, up 3
  5. Describe the transformation from y=∣x∣ to y=∣x+1∣−2 using vertical stretches, reflections and shifts.left 1, down 2

  1. Describe horizontal stretches and reflections

    Describe the transformation from y=x3 to y=(12x)3 as a horizontal stretch or shrinkhorizontal stretch by a factor of 2
  2. Describe the transformation from y=x2 to y=(3x)2 as a horizontal stretch or shrinkhorizontal shrink by a factor of 13
  3. Describe the transformation from y=x to y=−xreflection in the y-axis
  4. Describe the transformation from y=∣x∣ to y=∣13x∣ as a horizontal stretch or shrinkhorizontal stretch by a factor of 3
  5. Describe the transformation from y=x2 to y=(14x)2 as a horizontal stretch or shrinkhorizontal stretch by a factor of 4

  1. Name the parent function

    Name the parent function of
    y=− ⁣∣x−3∣    absolute value, y=∣x∣
  2. Name the parent function of
    y=3x−3+2    square root, y=x
  3. Name the parent function of
    y=−1x−2    reciprocal, y=1x
  4. Name the parent function of
    y=2x+13+4    cube root, y=x3
  5. Name the parent function of
    y=−(x−4)3−5    cubic, y=x3

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 Vertex (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 x - 3 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 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 → Center (−3,0)
Describe the transformation
Describe the transformation from y=x3 to y=(x+3)3 using vertical stretches, reflections and shifts. → left 3
Write the equation from the description
Write the equation of y=x3 after these moves: left 1, up 2. → y=(x+1)3+2
Horizontal stretches and y-axis reflections
Describe the transformation from y=x to y=−x → reflection in the y-axis
Name the parent function
Name the parent function of
y=−3x+2−5 → square root, y=x
A number inside the bars
Graph, and give the vertex: y=∣−3x−5∣+3 → Vertex (−53,3)opens up

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 6: graph the transformation, describe the transformation, write the equation from the description, horizontal stretches and y-axis reflections, name the parent function and a number inside the bars. 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 x - 3 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.