Transformation of Parent Functions

Transformation of Parent Functions

Remember that every number has an effect on the graph of the parent function.

Vertical Shifts

This allows our function to move UP and DOWN.

This occurs OUTSIDE parenthesis or outside the function.

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.

This occurs INSIDE parenthesis or inside the function.

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

$$y=\left|x+4\right|$$ compare to the absolute value function ? 

• shift up 4

• shift down 4

• shift left  4

• shift right 4

Reflection

When there is a negative sign in front of your function, it means to reflect over the X - AXIS!

Multiple Select

How does

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

• shift up 3

• shift down 3

• shift left 3

• reflection 

Stretch & Shrink

Multiple Choice

How does

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

• Shrink by  factor of (1/4) 

• stretch by a factor of (1/4) 

• no change 

Rational Exponents

Multi-step transformations

The challenge begins....

• absolute value function 

• stretch by a factor of 3

• shift left 1

• shift down 5
  

​Example.....

Multiple Choice

How does

$$y=2\left(x-5\right)^2$$ compare to the parent quadratic function?

• stretch by 2 and shift down 5 

• shrink by 2 and shift right 5

• shrink by 2 and shift left 5

• stretch by 2 and shift right 5

Multiple Select

How does

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

Select ALL that apply

• shift up 3

• shift down 3

• shift left 5

• reflection 

• Shift right 5

Multiple Choice

How does

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

(The cubic is one of other parent functions covered in semester 1)

• shift right 6

  and down 4

• shift left 6

  and down 4

• shift right 6

  and up 4

• shift left 6

  and up 4