Describe the transformation from y = x^3 to y = (2x)^3

horizontal shrink by a factor of 1/2

Describe the transformation from y = x^2 to y = (2x)^2

horizontal shrink by a factor of 1/2

Describe the transformation from y = x^2 to y = (4x)^2

horizontal shrink by a factor of 1/4

Describe the transformation from y = |x| to y = |3x|

horizontal shrink by a factor of 1/3

Worksheets · Algebra 1

Algebra 1 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.



Sigma Prep · sigmaprep.io/worksheets Name Parent Functions and Transformations Date Period Graph each function, or answer as asked. Graph $y = {(x - 3)}^{3} + 3$ -10-10-5-55510100 Describe the transformation from $y = x^{2}$ to $y = {(x + 1)}^{2} + 3$ Describe the transformation from $y = x^{3}$ to $y = {(2 x)}^{3}$ Name the parent function of $y = - ∣ x - 3 ∣$ Graph $y = x - 1$ -10-10-5-55510100 Describe the transformation from $y = x$ to $y = x + 1$ Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{- x}$ Name the parent function of $y = 3 x^{3} + 3$ Graph $y = x + 2$ -10-10-5-55510100 Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 2 ∣ - 1$ Describe the transformation from $y = x^{2}$ to $y = {(2 x)}^{2}$ Name the parent function of $y = - 3 \frac{1}{x - 3} - 3$ Graph $y = x - 2$ -10-10-5-55510100 Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 1 ∣ + 1$ Describe the transformation from $y = x^{2}$ to $y = {(4 x)}^{2}$ Name the parent function of $y = \frac{1}{2} x^{3} + 5$ Graph $y = {(x - 3)}^{3} - 3$ -10-10-5-55510100 Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 3 ∣ - 1$ Describe the transformation from $y = ∣ x ∣$ to $y = ∣ 3 x ∣$ Name the parent function of $y = 2 \sqrt{x + 3} + 4$ 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.

Graph $y = {(x - 3)}^{3} + 3$ -10-10-5-55510100
Describe the transformation from $y = x^{2}$ to $y = {(x + 1)}^{2} + 3$
Describe the transformation from $y = x^{3}$ to $y = {(2 x)}^{3}$
Name the parent function of $y = - ∣ x - 3 ∣$
Graph $y = x - 1$ -10-10-5-55510100
Describe the transformation from $y = x$ to $y = x + 1$
Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{- x}$
Name the parent function of $y = 3 x^{3} + 3$
Graph $y = x + 2$ -10-10-5-55510100
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 2 ∣ - 1$
Describe the transformation from $y = x^{2}$ to $y = {(2 x)}^{2}$
Name the parent function of $y = - 3 \frac{1}{x - 3} - 3$
Graph $y = x - 2$ -10-10-5-55510100
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 1 ∣ + 1$
Describe the transformation from $y = x^{2}$ to $y = {(4 x)}^{2}$
Name the parent function of $y = \frac{1}{2} x^{3} + 5$
Graph $y = {(x - 3)}^{3} - 3$ -10-10-5-55510100
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 3 ∣ - 1$
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ 3 x ∣$
Name the parent function of $y = 2 \sqrt{x + 3} + 4$



Sigma Prep · sigmaprep.io/worksheets Name Parent Functions and TransformationsAnswer keyVersion 1 Date Period Graph each function, or answer as asked. Graph $y = {(x - 3)}^{3} + 3$ -10-10-5-55510100Anchor at $(3, 3)$ Describe the transformation from $y = x^{2}$ to $y = {(x + 1)}^{2} + 3$ left 1, up 3 Describe the transformation from $y = x^{3}$ to $y = {(2 x)}^{3}$ horizontal shrink by a factor of $\frac{1}{2}$ Name the parent function of $y = - ∣ x - 3 ∣$ absolute value, $y = ∣ x ∣$ Graph $y = x - 1$ -10-10-5-55510100Anchor at $(0, - 1)$ Describe the transformation from $y = x$ to $y = x + 1$ up 1 Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{- x}$ reflection in the y-axis Name the parent function of $y = 3 x^{3} + 3$ cubic, $y = x^{3}$ Graph $y = x + 2$ -10-10-5-55510100Anchor at $(0, 2)$ Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 2 ∣ - 1$ left 2, down 1 Describe the transformation from $y = x^{2}$ to $y = {(2 x)}^{2}$ horizontal shrink by a factor of $\frac{1}{2}$ Name the parent function of $y = - 3 \frac{1}{x - 3} - 3$ reciprocal, $y = \frac{1}{x}$ Graph $y = x - 2$ -10-10-5-55510100Anchor at $(0, - 2)$ Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 1 ∣ + 1$ left 1, up 1 Describe the transformation from $y = x^{2}$ to $y = {(4 x)}^{2}$ horizontal shrink by a factor of $\frac{1}{4}$ Name the parent function of $y = \frac{1}{2} x^{3} + 5$ cubic, $y = x^{3}$ Graph $y = {(x - 3)}^{3} - 3$ -10-10-5-55510100Anchor at $(3, - 3)$ Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 3 ∣ - 1$ left 3, down 1 Describe the transformation from $y = ∣ x ∣$ to $y = ∣ 3 x ∣$ horizontal shrink by a factor of $\frac{1}{3}$ Name the parent function of $y = 2 \sqrt{x + 3} + 4$ square root, $y = \sqrt{x}$ 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.

Graph $y = {(x - 3)}^{3} + 3$ -10-10-5-55510100Anchor at $(3, 3)$
Describe the transformation from $y = x^{2}$ to $y = {(x + 1)}^{2} + 3$ left 1, up 3
Describe the transformation from $y = x^{3}$ to $y = {(2 x)}^{3}$ horizontal shrink by a factor of $\frac{1}{2}$
Name the parent function of $y = - ∣ x - 3 ∣$ absolute value, $y = ∣ x ∣$
Graph $y = x - 1$ -10-10-5-55510100Anchor at $(0, - 1)$
Describe the transformation from $y = x$ to $y = x + 1$ up 1
Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{- x}$ reflection in the y-axis
Name the parent function of $y = 3 x^{3} + 3$ cubic, $y = x^{3}$
Graph $y = x + 2$ -10-10-5-55510100Anchor at $(0, 2)$
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 2 ∣ - 1$ left 2, down 1
Describe the transformation from $y = x^{2}$ to $y = {(2 x)}^{2}$ horizontal shrink by a factor of $\frac{1}{2}$
Name the parent function of $y = - 3 \frac{1}{x - 3} - 3$ reciprocal, $y = \frac{1}{x}$
Graph $y = x - 2$ -10-10-5-55510100Anchor at $(0, - 2)$
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 1 ∣ + 1$ left 1, up 1
Describe the transformation from $y = x^{2}$ to $y = {(4 x)}^{2}$ horizontal shrink by a factor of $\frac{1}{4}$
Name the parent function of $y = \frac{1}{2} x^{3} + 5$ cubic, $y = x^{3}$
Graph $y = {(x - 3)}^{3} - 3$ -10-10-5-55510100Anchor at $(3, - 3)$
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ x + 3 ∣ - 1$ left 3, down 1
Describe the transformation from $y = ∣ x ∣$ to $y = ∣ 3 x ∣$ horizontal shrink by a factor of $\frac{1}{3}$
Name the parent function of $y = 2 \sqrt{x + 3} + 4$ square root, $y = \sqrt{x}$

How to do these

Graph $y = - 2 ∣ x - 3 ∣ + 1$

The parent is y = |x|, the V with its corner at the origin.
x - 3 moves it right 3, and + 1 moves it up 1, so the corner is at (3, 1).
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 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 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 $y = x^{3}$ to $y = {(x + 3)}^{3}$ → left 3
Write the equation from the description: Write the equation: $y = x^{3}$ left 3 → $y = {(x + 3)}^{3}$
Horizontal stretches and y-axis reflections: Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{- x}$ → reflection in the y-axis
Name the parent function: Name the parent function of $y = - 3 \sqrt{x + 2} - 5$ → square root, $y = \sqrt{x}$

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 1 is usually taken around 8th or 9th 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 5: graph the transformation, describe the transformation, write the equation from the description, horizontal stretches and y-axis reflections and name the parent function. Tick as many as you want and set how many of each, or let it spread them evenly.

Algebra 1 parent functions and transformations worksheet

Select your difficulty

Parent Functions and Transformations

Parent Functions and TransformationsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these parent functions and transformations worksheets free?+

Do the parent functions and transformations worksheets come with an answer key?+

Are these parent functions and transformations worksheets printable?+

What grade are these parent functions and transformations worksheets for?+

Can I get a different version of the same parent functions and transformations worksheet?+

Is this a free alternative to Kuta Software for parent functions and transformations?+

Can I choose how hard the parent functions and transformations questions are?+

What kinds of question are on a parent functions and transformations worksheet?+

What do students get wrong with parent functions and transformations?+