Transformation of Functions

Parent function:
 $f\left(x\right)=x^2$  
Describe how the following graph is related to the parent graph: $f\left(x\right)=-x^2+3$  
*more than one answer*

• Graph flips

• Graph shifts to the right

• Graph shifts to the left

• Graph shifts vertically

Parent function:
 $f\left(x\right)=\left|x\right|$  
Describe how the following graph is related to the parent graph: $f\left(x\right)=\left|x\right|+2$  

• Shifts right 2 units

• Shifts left 2 units

• Shifts up 2 units

• Shifts down 2 units

Parent function:
 $f\left(x\right)=\left|x\right|$  
Describe how the following graph is related to the parent graph: $f\left(x\right)=3\left|x\right|$  

• Compresses closer/ More narrow

• Gets wider 

• Shifts up

• Shifts down

Which is an example of a reflection across the x-axis/ flip of the graph?

• $f\left(x\right)=\sqrt{x-2}$

• $f\left(x\right)\ =\ -\sqrt{x-2}$

• $f\left(x\right)=\sqrt{x}-2$

• None of the above

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

Which is an example of a function shifting to the right 3 units

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

• $f\left(x\right)\ =-\ x^2-3$

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

• $f\left(x\right)=\ -\ x^2+3$

Parent function:
 $f\left(x\right)=\left|x\right|$  
Describe how the following graph is related to the parent graph: $f\left(x\right)=\frac{1}{2}\left|x\right|$  

• Compresses closer/ More narrow

• Gets wider 

• Shifts up

• Shifts down

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

Parent function:
 $f\left(x\right)=x^2$  
Describe how the following graph is related to the parent graph: $f\left(x\right)=4\left(x-2\right)^2$  
*more than one answer*

• Graph gets narrow

• Graph gets wider

• Graph shifts to the left

• Graph shifts to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Which is an example of a function shifting downward 2 units and to the right 3 units

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

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

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

•  $f\left(x\right)=\ -2\ x^2+3$ 

Tags

CCSS.HSF.BF.B.3

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

• horizontal shift right 5 units
• horizontal shift left 5 units
• vertical shift up 5 units
• vertical shift down 5 units

Tags

CCSS.HSF.BF.B.3

If the blue graph is
f(x) = x² 
the red must be...

• g(x) = (x + 3)²
• g(x) = (x - 3)²
• g(x) = x² + 3
• g(x) = x² - 2

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7