Transformations of Functions

Transformations of Functions

10-4 and 10-5

Multiple Choice

 Describe the translation that occurred: $m\left(x\right)=f\left(x+1\right)$ 

• Left 1

• Right 1

• Up 1

• Down 1

Multiple Choice

Describe the translation that occurred: $w\left(x\right)=f\left(x-7\right)$  

• Down 7

• Up 7

• Right 7

• Left 7

Multiple Choice

Describe the translation from the blue dotted graph to the red graph.

• $f\left(x-4\right)-3$

• $f\left(x-4\right)+3$

• $f\left(x+4\right)+3$

• $f\left(x+4\right)-3$

Multiple Choice

Which equation below is a quadratic that has been translated up 5 units?

•  $f\left(x\right)=x^2-5$  

•  $f\left(x\right)=x^2+5$  

•  $f\left(x\right)=\left(x-5\right)^2$  

•  $f\left(x\right)=\left(x+5\right)^2$  

•  $f\left(x\right)=\sqrt{x}+5$  

Open Ended

What do you notice about the graphs in the picture (and on the last slide)?

Reflections of f(x)

-f(x) is a function that has been reflected across the x-axis

Multiple Choice

Name the transformation from the function  $y=\sqrt{x}$   to the function   $y=-\sqrt{x+3}$  .

• Reflection over the y-axis, left 3.

• Reflection over the y-axis, right 3.

• Reflection over the x-axis, left 3.

• Reflection over the x-axis, right 3.

Multiple Choice

Which function shows a reflection over the x-axis and a shift right 3 units?

• $-f\left(x-3\right)$

• $-f\left(x+3\right)$

• $f\left(-x+3\right)$

• $-f\left(x\right)-3$

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Multiple Choice

Describe the transformation that occurred: $s\left(x\right)=7f\left(x\right)$  

• Vertical Compression

• Up 7 units

• Over 7 units

• Vertical Stretch

Multiple Select

Which functions below represent a vertical compression? SELECT ALL THAT APPLY.

•  $2f\left(x\right)$  

•  $-\frac{1}{2}f\left(x\right)$  

•  $0.1f\left(x\right)$  

•  $-3.5f\left(x\right)$  

Multiple Choice

 $-f\left(x+3\right)+4$  

Describe the transformations:

• Shifted left 3 units
  Shifted up 4 units
  

• Reflection over the y-axis
  Shifted right 3 units
  Shifted up 4 units

• Shifted right 3 units
  Shifted up 4 units

• Reflection over the x-axis
  Shifted left 3 units
  Shifted up 4 units

Multiple Choice

Describe the transformation: $f\left(x\right)=\frac{1}{3}x^2+2$  

• Vertical compression by a factor of of 1/3
  Up 2

• Vertical stretch by a factor of 1/3
  Up 2

• reflection over the x-axis
  Up 2

• Vertical compression by a factor of of 1/3

  Right 2

Multiple Select

Describe the transformation: (click on two answers)

 $f\left(x\right)=-\left(x-7\right)^2$  

• Reflection over the x-axis

• Reflection over the y-axis

• Shift 7 units left

• Shift 7 units right