Transformations Recap (Shift & Reflect)

Transformations Recap

(Shift & Reflect)

Today we are going to review all the content from last week, including: parent functions, shifts vertically, shifts horizontally, and reflections.

Multiple Choice

Name the type of function pictured to the left.

• Linear

• Quadratic

• Absolute Value

• Square Root

Multiple Choice

If the parent function was

 $f\left(x\right)=x^2$  , describe the shift applied to graph $g\left(x\right)=x^2+14$  would be...

• Shift right 14 units

• Shift left 14 units

• Shift up 14 units

• Shift down 14 units

Summary:

Vertical Shifts

Values outside the parenthesis will always shift a function up or down from the origin.

Poll

Rate your understanding of vertical shifts of functions.

• Totally got it!

• Mostly get it!

• Still need some help

• Totally confused

Multiple Choice

Name the type of function pictured to the left.

• Linear

• Quadratic

• Absolute Value

• Square Root

Multiple Choice

If the given parent function is:

 $f\left(x\right)=\left|x\right|$  
Describe the shift in the graph of:  $r\left(x\right)=\left|x+5\right|$  

• shift up 5 units

• shift down 5 units

• shift left 5 units

• shift right 5 units

Summary:

Horizontal Shifts 

Values inside the parenthesis will always shift a function left or right away from the origin.

Shift will be the opposite of the value you see in the parenthesis.

Poll

Rate your understanding of horizontal shifts of functions.

• Totally got it!

• Mostly get it!

• Still need some help

• Totally confused

Multiple Choice

Given the parent function:

 $f\left(x\right)=x^2$  , what would a negative multiplied in front of the x-squared do to the graph? 

• Nothing

• Reflect the graph down (over the x-axis)

• Shift the graph down

Multiple Choice

Choose the correct graph below with a reflection of the parent function.

Summary:

Reflections

The flip of the graph is caused by a negative sign outside the function. 

Example: $f\left(x\right)=-\left|x+1\right|-2$  

The first negative sign is causing the graph to flip over and point down. 

Poll

Rate your understanding of reflections of functions.

• Totally got it!

• Mostly get it!

• Still need some help

• Totally confused