What transformations have occurred?

Reflected over x-axis and down 4 units

Reflected over x-axis and up 4 units

Reflected over x-axis and right 4 units

Reflected over x-axis and left 4 units

Alyssa graphed the absolute value parent function. Then, she reflected the graph over the x-axis, shifted it five units to the right and two units up. What is the new equation?

f ( x ) = − ∣ x − 5 ∣ + 2 f(x)=-\left|x-5\right|+2 f ( x ) = − ∣ x − 5 ∣ + 2

f ( x ) = ∣ x + 5 ∣ + 2 f(x)=\left|x+5\right|+2 f ( x ) = ∣ x + 5 ∣ + 2

f ( x ) = ∣ x − 5 ∣ − 2 f(x)=\left|x-5\right|-2 f ( x ) = ∣ x − 5 ∣ − 2

f ( x ) = − ∣ x + 5 ∣ + 2 f(x)=-\left|x+5\right|+2 f ( x ) = − ∣ x + 5 ∣ + 2

What is the equation to this graph?

f ( x ) = ∣ x + 2 ∣ + 1 f(x)=\left|x+2\right|+1 f ( x ) = ∣ x + 2 ∣ + 1

f ( x ) = ∣ x − 2 ∣ + 1 f(x)=\left|x-2\right|+1 f ( x ) = ∣ x − 2 ∣ + 1

f ( x ) = ∣ x + 2 ∣ − 1 f(x)=\left|x+2\right|-1 f ( x ) = ∣ x + 2 ∣ − 1

f ( x ) = ∣ x − 2 ∣ − 1 f(x)=\left|x-2\right|-1 f ( x ) = ∣ x − 2 ∣ − 1

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

y = − ∣ x − 15 ∣ − 3 y=-\left|x-15\right|-3 y = − ∣ x − 1 5 ∣ − 3

y = − ∣ x + 15 ∣ − 3 y=-\left|x+15\right|-3 y = − ∣ x + 1 5 ∣ − 3

y = 1 2 ∣ x + 3 ∣ − 15 y=\frac{1}{2}\left|x+3\right|-15 y = 2 1 ∣ x + 3 ∣ − 1 5

y = 1 2 ∣ x − 3 ∣ − 15 y=\frac{1}{2}\left|x-3\right|-15 y = 2 1 ∣ x − 3 ∣ − 1 5

y = ∣ − x − 15 ∣ − 3 y=\left|-x-15\right|-3 y = ∣ − x − 1 5 ∣ − 3

What does the transformation f ( x ) → f ( x + 1 ) − 9 f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9 f ( x ) → f ( x + 1 ) − 9 do to the graph of f ( x ) f\left(x\right) f ( x ) ?

translates it left one unit and down 9 units

translates it right one unit and down 9 units

translates it up one unit and right 9 units

translates it down one unit and left 9 units

What does the transformation f ( x ) → 1 3 f ( x ) + 4 f\left(x\right)\ \rightarrow\ \frac{1}{3}f\left(x\right)+4 f ( x ) → 3 1 f ( x ) + 4 do to the graph of f ( x ) f\left(x\right) f ( x ) ?

Shrinks the graph vertically by a factor of 1/3 and translates up 4 units.

Stretches the graph by a factor of 3 and translates up 4 units.

Translates the graph left 1/3 of a unit and up 4 units.

Translates the graph right 3 unites and down 4 units.

Write the equation for a graph that is vertically compressed by a factor of 2 5 \frac{2}{5} 5 2 and shifted right 6.

y = 2 5 ∣ x − 6 ∣ y=\frac{2}{5}\left|x-6\right| y = 5 2 ∣ x − 6 ∣

y = 6 ∣ x ∣ − 2 5 y=6\left|x\right|-\frac{2}{5} y = 6 ∣ x ∣ − 5 2

y = 2 5 ∣ x ∣ + 6 y=\frac{2}{5}\left|x\right|+\ 6 y = 5 2 ∣ x ∣ + 6

y = 2 5 ∣ x + 6 ∣ y=\frac{2}{5}\left|x+6\right| y = 5 2 ∣ x + 6 ∣

Let f ( x ) = x f\left(x\right)=\sqrt{x} 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"> and g ( x ) = − 3 x − 2 + 1 g\left(x\right)=-3\sqrt{x-2}+1 g ( x ) = − 3 x − 2 <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 . Describe g(x) in terms of f(x):

reflects over x axis, vertical stretch by 3, right 2, up 1

reflects over y axis, vertical compression by -3, left 2, up 1

reflects over x axis, vertical stretch by -3, left 2, up 1

reflects over y axis, vertical compression by 1/3, right 2, up 1

Resource Library

Math

Functions Operations

Parent Functions And Transformations

Test: Parent Functions And Transformations

Test: Parent Functions and Transformations

Authored by Dalila R

Mathematics

12th Grade

CCSS covered

Used 7+ times

Test: Parent Functions and Transformations

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26 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which parent function matches the graph?

y = |x|

y = x

y = x²

y = 2^x

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What type of function is shown?

linear

quadratic

square root

absolute value

Tags

CCSS.HSA.REI.D.10

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which equation below is a quadratic function translated up 5 units?

y = x² + 5

y = (x + 5)²

y = 5x²

y = -x² - 5

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

Which equation below is a quadratic function translated left 4 units?

y = x² + 4

y = (x + 4)²

y = (x - 4)²

y = 4x²

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

y = x² + 2

y = -x² + 2

y = x² - 2

y = -(x + 2)²

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Describe the transformation

left 2 units up 5 units

right 2 units up 5 units

left 2 units down 5 units

right 2 units down 5 units

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Tell how the graph transformed.
y = (x - 3)²

Translated right 3

Translated left 3

Translated up 3

Translated down 9

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

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