Describe the transformation from y = x^2 to y = -(x + 1)^2 + 4

reflected in the x-axis, left 1, up 4

Describe the transformation from y = x^3 to y = (1/2x)^3

horizontal stretch by a factor of 2

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

horizontal shrink by a factor of 1/3

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

reflected in the x-axis, right 2, down 3

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

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

Worksheets · Precalculus

Precalculus parent functions and transformations worksheet

Precalculus writes transformations in function notation, y = a f(b(x - h)) + k, and applies them to any function, not only the six parents. Horizontal stretches and moving single points through a transformation are the new skills.

Also taught in Algebra 2 and Algebra 1, 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.



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



Sigma Prep · sigmaprep.io/worksheets Name Parent Functions and TransformationsAnswer keyVersion 1 Date Period Graph each function, or answer as asked. Graph $y = ∣ x - 4 ∣ + 4$ Vertex $(4, 4)$ Describe the transformation from $y = x^{2}$ to $y = - {(x + 1)}^{2} + 4$ reflected in the $x$ -axis, left 1, up 4 Describe the transformation from $y = x^{3}$ to $y = {(\frac{1}{2} x)}^{3}$ horizontal stretch by a factor of $2$ Name the parent function of $y = - ⁣ ∣ x - 3 ∣$ absolute value, $y = ∣ x ∣$ Graph $y = - {(x + 2)}^{2} - 3$ Vertex $(- 2, - 3)$ Describe the transformation from $y = x$ to $y = - x + 3$ reflected in the $x$ -axis, up 3 Describe the transformation from $y = x^{2}$ to $y = {(3 x)}^{2}$ horizontal shrink by a factor of $\frac{1}{3}$ Name the parent function of $y = 3 \sqrt{x - 3} + 2$ square root, $y = \sqrt{x}$ Graph $y = 2 {(x + 2)}^{3} + 2$ Center $(- 2, 2)$ Describe the transformation from $y = x$ to $y = x - 2$ down 2 Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{- x}$ reflection in the $y$ -axis Name the parent function of $y = 3 \sqrt[3]{x + 4} + 4$ cube root, $y = \sqrt[3]{x}$ Graph $y = \sqrt{x - 3} - 2$ Starts at $(3, - 2)$ Describe the transformation from $y = \sqrt{x}$ to $y = - \sqrt{x - 2} - 3$ reflected in the $x$ -axis, right 2, down 3 Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{2 x}$ horizontal shrink by a factor of $\frac{1}{2}$ Name the parent function of $y = \frac{1}{2 (x - 2)} - 4$ reciprocal, $y = \frac{1}{x}$ Graph $y = ∣ x + 3 ∣ - 4$ Vertex $(- 3, - 4)$ Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{x - 3} + 1$ right 3, 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 $y = - {(x + 3)}^{2} + 4$ quadratic, $y = x^{2}$ 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 answer as asked.

Graph $y = ∣ x - 4 ∣ + 4$ Vertex $(4, 4)$
Describe the transformation from $y = x^{2}$ to $y = - {(x + 1)}^{2} + 4$ reflected in the $x$ -axis, left 1, up 4
Describe the transformation from $y = x^{3}$ to $y = {(\frac{1}{2} x)}^{3}$ horizontal stretch by a factor of $2$
Name the parent function of
$y = - ⁣ ∣ x - 3 ∣$ absolute value, $y = ∣ x ∣$
Graph $y = - {(x + 2)}^{2} - 3$ Vertex $(- 2, - 3)$
Describe the transformation from $y = x$ to $y = - x + 3$ reflected in the $x$ -axis, up 3
Describe the transformation from $y = x^{2}$ to $y = {(3 x)}^{2}$ horizontal shrink by a factor of $\frac{1}{3}$
Name the parent function of
$y = 3 \sqrt{x - 3} + 2$ square root, $y = \sqrt{x}$
Graph $y = 2 {(x + 2)}^{3} + 2$ Center $(- 2, 2)$
Describe the transformation from $y = x$ to $y = x - 2$ down 2
Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{- x}$ reflection in the $y$ -axis
Name the parent function of
$y = 3 \sqrt[3]{x + 4} + 4$ cube root, $y = \sqrt[3]{x}$
Graph $y = \sqrt{x - 3} - 2$ Starts at $(3, - 2)$
Describe the transformation from $y = \sqrt{x}$ to $y = - \sqrt{x - 2} - 3$ reflected in the $x$ -axis, right 2, down 3
Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{2 x}$ horizontal shrink by a factor of $\frac{1}{2}$
Name the parent function of
$y = \frac{1}{2 (x - 2)} - 4$ reciprocal, $y = \frac{1}{x}$
Graph $y = ∣ x + 3 ∣ - 4$ Vertex $(- 3, - 4)$
Describe the transformation from $y = \sqrt{x}$ to $y = \sqrt{x - 3} + 1$ right 3, 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
$y = - {(x + 3)}^{2} + 4$ quadratic, $y = x^{2}$

How to do these

$(6, 5)$ is on $y = f (x)$ . Find the matching point on $y = 3 f (2 (x - 1)) - 4$

Inside the f, solve 2(x - 1) = 6, so x = 4.
Outside, the height becomes 3 · 5 - 4 = 11.

The answer is $(4, 11)$ .

Where students go wrong

Reading f(2x - 6) as a shift of 6. Factor out the 2 first: f(2(x - 3)) squeezes the graph by a factor of 1/2 and then shifts it right 3.

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 $y = x^{3}$ to $y = {(x + 3)}^{3}$ → left 3
Write the equation from the description: Write the equation: $y = x^{3}$ left 1, up 2 → $y = {(x + 1)}^{3} + 2$
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, $y = \sqrt{x}$
A number inside the bars: Graph, and give the vertex: $y = ∣ - 3 x - 5 ∣ + 3$ → Vertex $(- \frac{5}{3}, 3)$ 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.

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 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.

Precalculus 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?+

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

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