What transformations has the function undergone?

reflect over x, vertical stretch by 2, right 5, up 1

reflect over y, vertical compression by 2, right 5, up 1

reflect over x, horizontal compression by 2, left 5, up 1

reflect over y, horizontal stretch by -2, right 5, up 1

Vertical compression by ⅓ and left 9

Vertical compression ⅓ and right 9

Horizontal stretch by 3 and left 9

Horizontal stretch by 3 and right 9

Vertically stretched by 6 and reflected over the y-axis

Vertically stretched by 6 and reflected over the x-axis

Vertically compressed by 6 and reflected over the y-axis

Vertically compressed by 6 and reflected over the x-axis

Identify the equation of the transformed graph.

f ( x ) = ∣ x − 2 ∣ f\left(x\right)\ =\ \left|x-2\right| f ( x ) = ∣ x − 2 ∣

f ( x ) = ∣ x + 2 ∣ f\left(x\right)\ =\ \left|x+2\right| f ( x ) = ∣ x + 2 ∣

f ( x ) = ∣ x + 2 ∣ + 2 f\left(x\right)\ =\ \left|x+2\right|+2 f ( x ) = ∣ x + 2 ∣ + 2

f ( x ) = ∣ x − 2 ∣ + 2 f\left(x\right)\ =\ \left|x-2\right|+2 f ( x ) = ∣ x − 2 ∣ + 2

Describe the transformation from the absolute value parent function.

Vertically compressed by 1 5 \frac{1}{5} 5 1 and translated down 4 units

Vertically stretched by 1 5 \frac{1}{5} 5 1 and translated up 4 units

Vertically stretched by 5 and translated down 4 units

Vertically compressed by 5 and translated up 4 units

Which of these Square Root functions has shifted left 3?

f ( x ) = x + 3 f\left(x\right)=\sqrt{x+3} f ( x ) = x + 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

f ( x ) = x + 3 f\left(x\right)=\sqrt{x}+3 f ( x ) = x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 3

f ( x ) = x − 3 f\left(x\right)\ =\sqrt{x}-3 f ( x ) = x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 3

f ( x ) = x − 3 f\left(x\right)=\sqrt{x-3} f ( x ) = x − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Which of these Square Root functions shifted right 5 and down 1?

f ( x ) = x − 5 − 1 f\left(x\right)=\sqrt{x-5}-1 f ( x ) = x − 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 1

f ( x ) = x − 5 + 1 f\left(x\right)=\sqrt{x-5}+1 f ( x ) = x − 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1

f ( x ) = x + 5 − 1 f\left(x\right)=\sqrt{x+5}-1 f ( x ) = x + 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 1

f ( x ) = x + 5 + 1 f\left(x\right)=\sqrt{x+5}+1 f ( x ) = x + 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1

What are the transformations of the function compared to the parent function f(x) = √x

Vertical Stretch by a factor of 2; translated down 5

Shifted right 2 units and down 5 units

Vertical stretch by a factor of 2; translated left

Vertical stretch by a factor of 2; translated right one

What function best describes this graph?

f ( x ) = x − 4 − 2 f\left(x\right)=\sqrt{x-4}-2 f ( x ) = x − 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2

f ( x ) = − x + 4 − 2 f\left(x\right)=-\sqrt{x+4}-2 f ( x ) = − x + 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2

f ( x ) = − x − 4 − 2 f\left(x\right)=-\sqrt{x-4}-2 f ( x ) = − x − 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2

f ( x ) = x + 4 + 2 f\left(x\right)=\sqrt{x+4}+2 f ( x ) = x + 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2

What are the transformations of this functions compared to the parent function?

Reflected over the x-axis, vertical stretch by 2, and shifted right 5

Shifted right 5, down 2, and reflected over the x-axis

Reflected over the x-axis, vertical stretch by 2, and shifted left 5

Function Transformations Review

Authored by Shannon Dorrell

Mathematics

11th - 12th Grade

CCSS covered

Used 114+ times

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25 questions

Show all answers

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Describe the transformation that occurred.
f(x) = (x - 7)²

Down 7

Up 7

Right 7

Vertically compressed by 7

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Describe the transformation that occurred
f(x) = x + 1

Left 1

Right 1

down 1

up 1

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What are the transformations of:

$f\left(x\right)\ =-\left(x-4\right)^3+2$

Reflect over x-axis, left 4, and up 2

Reflect over x-axis, right 4, and up 2

Reflect over y-axis, left 4, and up 2

Reflect over y-axis, right 4, and up 2

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Describe the transformation that occurred.
f(x) = x³ + 2

Down 2

Left 2

Up 2

Right 2

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

right 3, up 2, reflected across the y-axis

right 3, up 2, reflected across the x-axis

left 3, up 2, reflected across the y-axis

left 3, up 2, reflected across the x-axis

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which of the following is the equation for the cubic function graphed above

$y=\left(x+4\right)^3+3$

$y=\left(x+4\right)^3-3$

$y=\left(x-4\right)^3+3$

$y=\left(x-4\right)^3-3$

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Describe the transformation of the graph f(x) = -2(x + 5)³

Vertically compressed by 2, Reflected over y-axis, Right 5

Vertically stretched by 2, Reflected over x-axis, Left 5

Vertically stretched by 2, Reflected over x-axis, Right 5

Vertically compressed by 2, reflected over y-axis, Left 5

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What function has the transformations:
Left 4 and up 7

$f\left(x\right)\ =\ \left|x+4\right|+7$

$f\left(x\right)\ =\ \left(x-4\right)^2\ +\ 7$

$f\left(x\right)\ =\ \left(x+7\right)^2-\ 4$

$f\left(x\right)\ =\ \left|x+4\right|-7$

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What function has the transformations:
Vertical stretch by 7 and Reflected over x-axis

$f\left(x\right)\ =\ -7x^2$

$f\left(x\right)\ =\ 7\left|-x\right|$

$f\left(x\right)\ =\ \sqrt{-7x}$

$f\left(x\right)\ =\ -\left|7x\right|$

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

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Function Transformations Review

Describe the transformation that occurred.f(x) = (x - 7)2

Describe the transformation that occurredf(x) = x + 1

What are the transformations of: f(x) =−(x−4)3+2f\left(x\right)\ =-\left(x-4\right)^3+2f(x) =−(x−4)3+2

Describe the transformation that occurred.f(x) = x3 + 2

If f(x) = x3 is changed to f(x) = - (x + 3)3 + 2, how is the graph transformed?

Which of the following is the equation for the cubic function graphed above

Describe the transformation of the graph f(x) = -2(x + 5)3

What transformations has the function undergone?

What function has the transformations:Left 4 and up 7

What function has the transformations:Vertical stretch by 7 and Reflected over x-axis

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Describe the transformation that occurred.
f(x) = (x - 7)²

Describe the transformation that occurred
f(x) = x + 1

What are the transformations of:

$f\left(x\right)\ =-\left(x-4\right)^3+2$

Describe the transformation that occurred.
f(x) = x³ + 2

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

Describe the transformation of the graph f(x) = -2(x + 5)³

What function has the transformations:
Left 4 and up 7

What function has the transformations:
Vertical stretch by 7 and Reflected over x-axis