Parent Functions and Transformations

​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 

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

Multiple Choice

Describe the transformation

• left 2 up 5

• right 2 up 5

• left 2 down 5

• right 2 down 5

Multiple Choice

Write the equation to match the graph. The parent function is y=|x|

• y = Ix + 2I - 1

• y = -Ix + 2I - 1

• y = -Ix - 2I - 1

• y = -Ix + 1I - 2

Multiple Choice

Describe the transformation from the parent graph

• Reflect over x, right 3, down 4

• Reflect over y, right 3, down 4

• Reflect over x, right 3, up 4

• Reflect over y, left 3, down 4

Multiple Choice

What is the equation of the PARENT  function?

• f(x) = 2^x

• f(x) = x³

• f(x) = |x|

• f(x) = x

Multiple Choice

What type of function is shown?

• cube root

• square root

• logarithm

• exponential