Transformations of Parent Functions

Transformations of Parent Functions

Vertical translations, horizontal translations, reflections, vertical stretches, vertical shrinks

​First, let's review parent functions!

Multiple Choice

What type of function is shown?

• absolute value

• quadratic

• linear

• exponential

Multiple Choice

What type of function is shown?

• linear

• quadratic

• square root

• absolute value

Multiple Choice

What type of function is shown?

• exponential

• linear

• quadratic

• square root

Multiple Choice

Which parent function matches the graph?

• f(x) = √(x)

• f(x) = ∛(x)

• f(x) = |x|

• f(x) = a⋅b^x

Multiple Choice

Name the parent function. 

• constant

• square root

• linear

• absolute value

​Now, let's move!

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

Multiple Choice

Which transformation on

f(x) = x

is g(x) = -f(x)

• Reflection across the y-axis

• The slope will be less steep

• The graph will be wider

• Reflection across 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 

Multi-Step Transformations

Let's put it all together!​

• Vertical Translations

• Horizontal Translations

• Reflections

• Vertical Stretches

• Vertical Shrinks​

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