Transformation of Parent Functions

Transformation of Parent Functions

I would go ahead and pull up Desmos graphing calculator.

Vertical Shifts

This allows our function to move UP and DOWN or vertically.

These are outside of the parenthesis!!

Multiple Choice

How does

 $y=\left|x\right|-5$  compare to the absolute value parent function? 

• shift up 5

• shift down 5 

• shift left 5 

• shift right 5 

Horizontal Shifts

This allows our function to move LEFT and RIGHT or horizontally.

This occurs INSIDE parenthesis.

Multiple Choice

How does

 $y=\left(x-2\right)^2$  compare to the quadratic parent function? 

• shift up 2

• shift down 2

• shift left 2 

• shift right 2

Multiple Choice

How does

 $y=\sqrt{\left(x+4\right)}$  compare to the radical function ? 

• shift up 4

• shift down 4

• shift left  4

• shift right 4

Reflection

When there is a negative sign in front of your equation this means to reflect over the X - AXIS!

Multiple Select

How does

 $f\left(x\right)=-x^3+3$  compare to the cubic parent function? Select TWO

• vertical shift up 

• vertical shift down 

• horizontal shift left 

• reflection 

Stretch & Compression

• If a > 1 : There is a STRETCH

  
  

• If 0 < a < 1 : There is a COMPRESSION

Multiple Choice

How does

 $y=\frac{\text{1}}{\text{4}}\left|x\right|$  compare to the absolute value  function ? 

• compression by  factor of (1/4) 

• stretch by a factor of (1/4) 

• no change 

Multi-step transformations

Let's pull it together

 $g\left(x\right)=-\left(x+4\right)^2+6$  

• quadratic function
  

• horizontal shift left 4 

• vertical shift up 6 

• reflection
  

 $y=3\left|x+1\right|-5$  

• absolute value function 
  

• stretch by a factor of 3
  

• horizontal shift left 1
  

• vertical shift down 5
  

Multiple Choice

How does

 $y=2\sqrt{\left(x-5\right)}$  compare to the square root function? 

• stretch and vertical shift down 5 

• compression and horizontal shift right 

• compression and horizontal shift left

• stretch and horizontal shift right 

Multiple Select

How does

 $f\left(x\right)=-\left|x+5\right|-3$  compare to the absolute value parent function? Select ALL that apply

• vertical shift up 

• vertical shift down 

• horizontal shift left 

• reflection 

• horizontal shift right

Multiple Choice

How does

 $y=\left(x+6\right)^3-4$  compare to the cubic function? 

• horizontal shift right and down
  

• horizontal shift left and down
  

• horizontal shift right and up
  

• horizontal shift left and up
  

Quadratic transformations

• orange:  $y=\left(x+3\right)^2-1$  
  

• blue:  $y=\left(x+3\right)^2+1$  
  

• green  $y=\left(x-3\right)^2-1$  
  

• red quadratic function