Function Transformations: The basics

 $g\left(x\right)=3f\left(x\right)$  

• vertical shift up 3

• horizontal shift 3 to the right

• vertical stretch by factor of 3

• vertical compression by factor of 3

Tags

CCSS.HSF.BF.B.3

 $g\left(x\right)=f\left(x+4\right)$  

• horizontal shift 4 to the left

• horizontal shift 4 to the right

• vertical shift up 4

• vertical shift down 4

• vertical stretch by factor of 4

Tags

CCSS.HSF.BF.B.3

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

• vertical stretch by 7

• horizontal shift 7 to right

• horizontal shift 7 to left

• vertical shift 7 up

• vertical shift 7 down

Tags

CCSS.HSF.BF.B.3

 $g\left(x\right)=f\left(x\right)+6$  

• vertical stretch by 6

• vertical shift up 6

• horizontal shift 6 right

• horizontal shift 6 left

• vertical shift down 6

Tags

CCSS.HSF.BF.B.3

 $g\left(x\right)=f\left(x\right)-1$  

• vertical stretch by factor of -1

• vertical shift down 1

• vertical shift up 1

• horizontal shift left 1

• horizontal shift right 1

Tags

CCSS.HSF.BF.B.3

 $g\left(x\right)=-f\left(x\right)$  

• reflect over the x-axis

• reflect over the y-axis

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

 $g\left(x\right)=\frac{1}{2}f\left(x\right)$  

• vertical stretch by a factor of 1/2

• vertical compression by a factor of 1/2

• vertical shift to the right by 1/2

• vertical shift to the left by 1/2

Tags

CCSS.HSF.BF.B.3