Function Transformations

Multiple Choice

Name the parent function. 

• constant
• square root
• linear
• absolute value

Multiple Choice

Which parent function matches the graph?

• f(x) = √(x)
• f(x) = ∛(x)
• f(x) = |x|
• f(x) = a⋅b^x

Multiple Choice

Which parent function matches the graph? 

• f(x) = a⋅b^x
• f(x) = ∛(x)
• f(x) = √(x)
• f(x) = x²

Multiple Choice

Which parent function matches the graph? 

• f(x) = x
• f(x) = x²
• f(x) =√(x)
• f(x) =∛(x)

Multiple Choice

What type of function is shown?

• Exponential 
• square root
• quadratic
• cube root

Multiple Choice

Which parent function matches the graph?

• f(x) = x
• f(x)= x²
• f(x) = |x|
• f(x) = ab^x

​Vertical Translation

​This allows our function to move UP or DOWN

​

​** These are outside of the parentheses **

​​

​+ k shifts up​

– k shifts down​

Multiple Choice

Describe the transformation from the parent absolute value function:

$$y=\left|x\right|-5$$  

• Shift up 5 units

• Shift down 5 units

• Shift right 5 units

• Shift left 5 units

​Horizontal Translation

This allows our function to move LEFT or RIGHT

​

​** These are inside the parentheses **

​

(x – h) shifts right

(x + h) shifts left

Multiple Choice

Describe the transformation from the parent quadratic function:

$$y=\left(x-2\right)^2$$  

• Shift up 2 units

• Shift down 2 units

• Shift right 2 units

• Shift left 2 units

Multiple Choice

Describe the transformation from the parent square root function:

$$y=\sqrt[]{x+4}$$  

• Shift up 4 units

• Shift down 4 units

• Shift right 4 units

• Shift left 4 units

Reflection

When there is a negative sign in front of the equation, this means the function is being reflected over the x-axis!​

Multiple Select

Describe the transformation from the parent cubic function:

$$y=-x^3+3$$  

* Select TWO answers *

• Shift up 3 units

• Shift down 3 units

• Reflection over the y-axis

• Reflection over the x-axis

Vertical Stretch and Vertical Shrink​

Makes the graph more narrow or more wide

​

​a > 1 = Vertical Stretch

0 < a < 1 = Vertical Shrink

Multiple Choice

Describe the transformation from the parent quadratic function:

$$y=\frac{1}{4}x^2$$  

• Vertical stretch by a factor of ¼

• Vertical shrink by a factor of ¼

Multiple Choice

Describe the transformation from the parent absolute value function:

$$y=8\left|x\right|$$  

• Vertical stretch by a factor of 8 

• Vertical shrink by a factor of 8 

Multiple Choice

 

Describe the transformation that occurred

p(x) = f(x + 3)

• Right 3 units

• Vertical Stretch

• Up 3 units

• Left 3 units

Multiple Choice

 

Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Stretch

• right 2 units

Multiple Choice

 Given g(x) = f(x-3) + 5.  What transformations took place from the original function f(x)?

• Left 3 up 5

• Right 3 down 5

• Left 3 down 5

• Right 3 up 5

Multiple Select

Describe the transformation of the equation below from the absolute value parent function. SELECT ALL THAT APPLY $$g\left(x\right)=\frac{1}{2}f\left(x+3\right)-2$$  

• right 3

• left 3

• Down 2

• Shrink by 1/2

• stretch by 2

Multiple Choice

If g(x) is a transformation of f(x), describe the transformation.

$$f\left(x\right)=2^x$$      $$g\left(x\right)=2^x+4$$   

• Up 4 units

• Down 4 units

• Left 4 units

• Right 4 units

Multiple Choice

If the blue function is f(x)=x², then the red function must be

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Multiple Choice

Which transformation transforms the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a vertical translation 4 units up
• a vertical translation 4 units down
• a horizontal translation 4 units to the left
• a horizontal translation 4 units to the right

Multiple Choice

Describe the transformation that occurred

s(x) = 7f(x)

• vertical compression

• Up 7 Units

• Over 7 Units

• vertical stretch

Multiple Select

Describe the transformation from the parent square root function:

$$y=2\ \sqrt[]{x-5}$$  

* Select TWO answers *

• Vertical stretch

• Vertical shrink

• Translation 5 units right

• Translation 5 units left

Multiple Select

Describe the transformation from the parent absolute value function:

$$y=-\left|x+4\right|-3$$  

* Select THREE answers *

• Reflection over the x-axis

• Translation 4 units left

• Translation 4 units up

• Translation 3 units left

• Translation 3 units down

Multiple Select

Describe the transformation from the parent cubic function:

$$y=\left(x+6\right)^3-4$$  

* Select TWO answers *

• Translation 6 units right

• Translation 6 units left

• Translation 4 units up

• Translation 4 units down

Multiple Choice

Describe the transformation that occurred
f(x - 4)

• Vertical
• Horizontal
• Both
• Neither