Exponential Transformations

Exponential Transformations

OBJ: SWBAT identify, describe and create functions from transformations

 $y\ =\ a\left(b\right)^{\left(x-h\right)}+k$  

Warm Up: Code - 886823

 $y=a\left(b\right)^{\left(x-h\right)}+k$  

 $y\ =\ k\ +\ a\left(b\right)^{\left(x-h\right)}$  

Multiple Choice

What is the transformation?

• Vertical Translation up 2
• Vertical Translation down 2
• Horizontal Translation left 2
• Horizontal Translation right 2

Multiple Choice

What is the transformation?

• Vertical Translation up 1
• Vertical Translation down 1
• Horizontal Translation left 1
• Horizontal Translation right 1

Multiple Choice

What is the transformation?

• Vertical Translation up 2 and Horizontal translation right 1
• Vertical Translation down 2 and Horizontal Translation left 1
• Horizontal Translation left 2 and Vertical Translation up 1
• Horizontal Translation right 2 and Vertical Translation down 1

Multiple Choice

Which graph best represents

 $y=2^x-4$  

Multiple Select

How did the graph transform from the parent function?

y=-5(2)^(x)

• Down 5

• Vertical Stretch by 5

• Left 2

• Right 2

• Flipped/Reflected over the x-axis

Multiple Choice

What is the a-value of the function?

• 4

• 3

• 2

• 1

Multiple Choice

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

• Vertically stretched by a factor of 2, right 3, and up 1

• Vertically compressed by a factor of 1/2, left 3 and down 1

• Vertically compressed by a factor of 1/2, right 3, and down 1

• Vertically stretched by a factor of 2, left 3, and up 1

Multiple Choice

Which of the following describes the transformation of  $f\left(x\right)=\frac{1}{2}\cdot2^{\left(x+2\right)}-3$  from the parent graph  $g\left(x\right)=2^x$  

• Vertically shift down 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift up 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift down 3, horizontally shift right 2, and vertically compressed 1/2 units

• Vertically shift up 3, horizontally shift right2, and vertically compressed 1/2 units

Multiple Select

Which of the following are TRUE about the function? (Choose all that apply)

• The exponential decay has been reflected.

• The exponential growth has been reflected.

• The function has been shifted down 2 units.

• The function has an growth rate of 2.

Multiple Select

 If g(x) is a transformation of f(x), describe the transformation.

 $f\left(x\right)=\left(\frac{2}{3}\right)^{-x}$  
 $g\left(x\right)=\left(\frac{2}{3}\right)^x$  

• Horizontal reflection

• Vertical reflection

• Reflect across the x-axis

• Reflect across the y-axis