Transformations of Absolute Value Functions

• Left 3

• Right 3

• Up 3

• Down 3

Answer explanation

The value inside the absolute value bars is the left/right movement. You must change the sign inside. After changing the sign, if the value is positive, it shifts right. If the value is negative, it shifts left.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

• Left 7

• Right 7

• Up 7

• Down 7

Answer explanation

The value outside of the absolute value bars is the up/down movement. You keep the sign. If the value is positive, it shifts up. If the value is negative, it shifts down.

Tags

CCSS.HSF.BF.B.3

• Left 5

  Down 1

• Right 5

  Down 1

• Left 5

  Up 1

• Right 5

  Up 1

• Left 1

  Down 5

Answer explanation

The value inside the absolute value bars is the left/right movement. You must change the sign inside. After changing the sign, if the value is positive, it shifts right. If the value is negative, it shifts left.

The value outside of the absolute value bars is the up/down movement. You keep the sign. If the value is positive, it shifts up. If the value is negative, it shifts down.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

• Right 3

  Down 8

• Right 3

  Up 8

• Left 3

  Down 8

• Left 3

  Up 8

• Up 3

  Right 8

Answer explanation

The value inside the absolute value bars is the left/right movement. You must change the sign inside. After changing the sign, if the value is positive, it shifts right. If the value is negative, it shifts left.

The value outside of the absolute value bars is the up/down movement. You keep the sign. If the value is positive, it shifts up. If the value is negative, it shifts down.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

• Left 4

  Up 2

• Left 4

  Down 2

• Right 4

  Up 2

• Right 4

  Down 2

• Right 2

  Down 4

Answer explanation

The value inside the absolute value bars is the left/right movement. You must change the sign inside. After changing the sign, if the value is positive, it shifts right. If the value is negative, it shifts left.

The value outside of the absolute value bars is the up/down movement. You keep the sign. If the value is positive, it shifts up. If the value is negative, it shifts down.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

• Right 4

  Down 2

• Right 4

  Up 2

• Left 4

  Down 2

• Left 4

  Up 2

• Left 2

  Up 4

Answer explanation

The value inside the absolute value bars is the left/right movement. You must change the sign inside. After changing the sign, if the value is positive, it shifts right. If the value is negative, it shifts left.

The value outside of the absolute value bars is the up/down movement. You keep the sign. If the value is positive, it shifts up. If the value is negative, it shifts down.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

• f(x) opens up (has a minimum) while

  g(x) opens down (has a maximum)

• f(x) opens down (has a maximum) while

  g(x) opens up (has a minimum)

• There is no difference

Answer explanation

A negative sign in front of the absolute value bars means the graph opens down (has a maximum).

No sign in front of the absolute value bars means the graph opens up (has a minimum).

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.C.9

• f(x) opens down (has a maximum) while g(x) opens up (has a minimum)

• f(x) opens up (has a minimum) while g(x) opens down (has a maximum)

• There is no difference

Answer explanation

A negative sign in front of the absolute value bars means the graph opens down (has a maximum).

No sign in front of the absolute value bars means the graph opens up (has a minimum).

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.IF.C.9

Given the graph of f(x) below, write the equation of g(x) that is shifted down 6 and right 3.

Tags

CCSS.HSF.BF.B.3

Given the graph of f(x) below, write the equation of g(x) that is shifted left 6 and up 5.

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7