Log and Exponential Transformations

 Describe the A-VALUE transformations from the parent function to $f\left(x\right)=2\log\left(x+4\right)-9$ 

• shrink by a factor of 2

• shift up 9 units

• stretch by a factor of 2

• shift right 4 units

 Describe the A-VALUE transformations from the parent function to $f\left(x\right)=\frac{1}{3}\left(4^x\right)-3$ 

• shrink by a factor of 1/3

• shift up 3 units

• stretch by a factor of 4

• shift right 4 units

 Describe the H-VALUE transformations from the parent function to $f\left(x\right)=5\left(4^{x-6}\right)+2$ 

• stretch by a factor of 5

• shift right 6 units

• stretch by a factor of 4

• shift left 6 units

 Describe the H-VALUE transformations from the parent function to $f\left(x\right)=2\log\left(x+4\right)-9$ 

• shift left 4 units

• shift up 9 units

• stretch by a factor of 2

• shift right 4 units

 Describe the K-VALUE transformations from the parent function to $f\left(x\right)=5\left(4^{x-6}\right)+2$ 

• stretch by a factor of 5

• shift right 6 units

• shift up 2 units

• shift down 2 units

 Describe the K-VALUE transformations from the parent function to $f\left(x\right)=\frac{1}{2}\log\left(x-3\right)+1$ 

• shift left 3 units

• shift up 1 unit

• stretch by a factor of 1/2

• shift right 1 units

 $f\left(x\right)=2^x$  

Given the parent function , write a new function  whose graph is stretched by a factor of 6 and shifted right 8 units.

•  $f\left(x\right)=6\left(2^{x-8}\right)$  

•  $f\left(x\right)=8\left(2^{x-6}\right)$  

•  $f\left(x\right)=6\left(4^{x-8}\right)$  

•  $f\left(x\right)=\left(2^{x-8}\right)$  

 $f\left(x\right)=5^x$  

Given the parent function , write a new function  whose graph is reflected over the x-axis and shifted left 2 units and shifted up 16 units.  

•  $f\left(x\right)=-\left(5^{x-8}\right)$  

•  $f\left(x\right)=-\left(5^{x-2}\right)+16$  

•  $f\left(x\right)=-\left(5^{x+2}\right)+16$  

•  $f\left(x\right)=-\left(5^{x-2}\right)-16$  

 $f\left(x\right)=\log x$  

Given the parent function , write a new function  whose graph is shifted left 5 units and shifted down 8 units.

•  $f\left(x\right)=-\log\left(x-5\right)-8$  

•  $f\left(x\right)=-\log\left(x+5\right)+8$  

•  $f\left(x\right)=\log\left(x-5\right)-8$  

•  $f\left(x\right)=\log\left(x+5\right)-8$  

 $f\left(x\right)=\log x$  

Given the parent function , write a new function  whose graph is compressed by a factor of ½ shifted right 7 units and shifted down 5 units.

•  $f\left(x\right)=\frac{1}{2}\log\left(x-7\right)-5$  

•  $f\left(x\right)=\frac{-1}{2}\log\left(x-7\right)-5$  

•  $f\left(x\right)=\frac{1}{2}\log\left(x+7\right)-5$  

•  $f\left(x\right)=\frac{1}{2}\log\left(x-7\right)+5$