This exponential function has a vertical stretch of 2 and a vertical shift up 7.

y = 2 ( 3 ) x + 7 y=2\left(3\right)^x+7 y = 2 ( 3 ) x + 7

y = 2 ( 3 ) ( x + 7 ) y=2\left(3\right)^{\left(x+7\right)} y = 2 ( 3 ) ( x + 7 )

y = 2 ( 3 ) x − 7 y=2\left(3\right)^x-7 y = 2 ( 3 ) x − 7

This exponential function has a flip over the x-axis, a decay rate of 1/3, and a horizontal shift right 3 units.

y = − ( 1 3 ) ( x − 3 ) y=-\left(\frac{1}{3}\right)^{\left(x-3\right)} y = − ( 3 1 ) ( x − 3 )

y = − ( 1 3 ) x + 3 y=-\left(\frac{1}{3}\right)^x+3 y = − ( 3 1 ) x + 3

y = − 1 3 x + 3 y=-\frac{1}{3}x+3 y = − 3 1 x + 3

y = ( 1 3 ) ( x + 3 ) y=\left(\frac{1}{3}\right)^{\left(x+3\right)} y = ( 3 1 ) ( x + 3 )

This exponential function has a flip over the x-axis, a vertical stretch of 7, a decay rate of 1/4, a horizontal shift left 2, and a vertical shift down 1.

y = − 7 ( 1 4 ) ( x + 2 ) − 1 y=-7\left(\frac{1}{4}\right)^{\left(x+2\right)}-1 y = − 7 ( 4 1 ) ( x + 2 ) − 1

y = − 1 4 ( 7 ) ( x − 2 ) − 1 y=-\frac{1}{4}\left(7\right)^{\left(x-2\right)}-1 y = − 4 1 ( 7 ) ( x − 2 ) − 1

y = − 7 ( 1 4 ) ( x − 1 ) + 2 y=-7\left(\frac{1}{4}\right)^{\left(x-1\right)}+2 y = − 7 ( 4 1 ) ( x − 1 ) + 2

y = 1 4 x + 1 y=\frac{1}{4}x+1 y = 4 1 x + 1

This linear function has a flip over the x-axis, a vertical shrink of 2/3 and a vertical shift down 4 units.

y = − 2 3 x − 4 y=-\frac{2}{3}x-4 y = − 3 2 x − 4

y = 2 3 x + 4 y=\frac{2}{3}x+4 y = 3 2 x + 4

y = − 4 x + 3 2 y=-4x+\frac{3}{2} y = − 4 x + 2 3

y = 2 3 ( 2 ) x − 4 y=\frac{2}{3}\left(2\right)^x-4 y = 3 2 ( 2 ) x − 4

This exponential function has a reflection across the x-axis, a vertical shrink of 1/2, a growth of 9, a horizontal shift right 7, and a vertical shift up 2.

y = − 1 2 ( 9 ) ( x − 7 ) + 2 y=-\frac{1}{2}\left(9\right)^{\left(x-7\right)}+2 y = − 2 1 ( 9 ) ( x − 7 ) + 2

y = − 9 ( 1 2 ) ( x − 7 ) + 2 y=-9\left(\frac{1}{2}\right)^{\left(x-7\right)}+2 y = − 9 ( 2 1 ) ( x − 7 ) + 2

y = − 1 2 ( 9 ) ( x + 7 ) − 2 y=-\frac{1}{2}\left(9\right)^{\left(x+7\right)}-2 y = − 2 1 ( 9 ) ( x + 7 ) − 2

y = 1 2 ( 9 ) ( x − 2 ) + 7 y=\frac{1}{2}\left(9\right)^{\left(x-2\right)}+7 y = 2 1 ( 9 ) ( x − 2 ) + 7

This exponential function has a vertical stretch of 4, a decay rate of 1/3, a horizontal shift left 8, and a vertical shift down 1.

y = 4 ( 1 3 ) ( x + 8 ) − 1 y=4\left(\frac{1}{3}\right)^{\left(x+8\right)}-1 y = 4 ( 3 1 ) ( x + 8 ) − 1

y = 4 ( 1 3 ) ( x + 1 ) − 8 y=4\left(\frac{1}{3}\right)^{\left(x+1\right)}-8 y = 4 ( 3 1 ) ( x + 1 ) − 8

y = 1 3 ( 4 ) ( x + 8 ) − 1 y=\frac{1}{3}\left(4\right)^{\left(x+8\right)}-1 y = 3 1 ( 4 ) ( x + 8 ) − 1

y = 4 ( 1 3 ) ( x − 8 ) + 1 y=4\left(\frac{1}{3}\right)^{\left(x-8\right)}+1 y = 4 ( 3 1 ) ( x − 8 ) + 1

This linear function has a reflection across the x-axis, a vertical stretch of 7 and a vertical shift down 4.

y = − 7 x − 4 y=-7x-4 y = − 7 x − 4

y = − 4 x + 7 y=-4x+7 y = − 4 x + 7

y = − 4 x − 7 y=-4x-7 y = − 4 x − 7

This linear function has a vertical shrink of 1/5 and a vertical shift up 9.

y = 1 5 x + 9 y=\frac{1}{5}x+9 y = 5 1 x + 9

y = − 1 5 x − 9 y=-\frac{1}{5}x-9 y = − 5 1 x − 9

y = 5 x − 9 y=5x-9 y = 5 x − 9

Transformations of Linear and Exponential Functions

Authored by Alicia Dunlap

Mathematics

9th - 12th Grade

CCSS covered

Used 35+ times

Transformations of Linear and Exponential Functions

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MULTIPLE SELECT QUESTION

45 sec • 1 pt

Check all that apply:
This exponential function has...

vertical shift up

horizontal shift left

exponential decay

exponential growth

vertical shrink

Tags

CCSS.HSF.BF.B.3

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Check all that apply:
This exponential function has...

exponential decay

vertical shift up

vertical shift down

exponential growth

Flip over the x-axis

Tags

CCSS.HSF-IF.C.7E

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Check all that apply:
This exponential function has...

exponential growth

horizontal shift left

vertical stretch

vertical shift down

flip over the x-axis

Tags

CCSS.HSF.BF.B.3

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Check all that apply:
This exponential function has...

exponential decay

reflect over the x-axis

vertical shift up

horizontal shift right

vertical shrink

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Check all that apply:
This exponential function has...

vertical stretch

horizontal shift right

vertical shift down

flip over the x-axis

exponential decay

Tags

CCSS.HSF.BF.B.3

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Check all that apply:
This exponential function has...

vertical stretch

flip over the x-axis

horizontal shift left

exponential growth

vertical shift up

Tags

CCSS.HSF.BF.B.3

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Check all that apply:
This linear function has...

vertical shrink

flip over the x-axis

vertical shift up

horizontal shift up

vertical shift down

Tags

CCSS.HSF.BF.B.3

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Transformations of Linear and Exponential Functions

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