Transformations of Exponential Functions "h"

GIven a parent function like  $f\left(x\right)=5^x$  , how does the h in  $g\left(x\right)=5^{x-h}$  affect the parent function?

• Translates the parent function horizontally (left or right)

• Translates the parent function vertically (up or down)

What transformation maps  $f\left(x\right)=2^x$  to  $g\left(x\right)=2^{x-8}$  

• Translates left 8 units

• Translates right 8 units

• Translates up 8 units 

• Translates down 8 units

What transformation maps  $f\left(x\right)=3^x$  to  $g\left(x\right)=3^{x+2}$  

• Translates left 2 units

• Translates right 2 units

• Translates up 2 units 

• Translates down 2 units

What transformation maps  $f\left(x\right)=\left(\frac{2}{5}\right)^x$  to  $g\left(x\right)=\left(\frac{2}{5}\right)^{x+6}$  

• Translates left 6 units

• Translates right 6 units

• Translates up 6 units 

• Translates up 2/5 units

What transformation maps  $f\left(x\right)=7^x$  to  $g\left(x\right)=7^{x-4}$  

• Translates left 4 units

• Translates right 4 units

• Translates up 7 units 

• Translates down 4 units

If the parent function  $f\left(x\right)=7^x$  is translated right 3 units, what would the equation of the resulting function be?

•  $g\left(x\right)=7^x+3$  

•  $g\left(x\right)=7^{x-3}$  

•  $g\left(x\right)=7^{x+3}$  

•  $g\left(x\right)=3\cdot7^x$  

If the parent function  $f\left(x\right)=\left(\frac{1}{3}\right)^x$  is translated right 2 units, what would the equation of the resulting function be?

•  $g\left(x\right)=\left(\frac{1}{3}\right)^x+2$  

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

•  $g\left(x\right)=\left(\frac{1}{3}\right)^{x+2}$  

•  $g\left(x\right)=\left(\frac{1}{3}\right)^{x-2}$  

If the parent function  $f\left(x\right)=2^x$  is translated left 8 units, what would the equation of the resulting function be?

•  $g\left(x\right)=2^{x-8}$  

•  $g\left(x\right)=2^{x+8}$  

•  $g\left(x\right)=2^x+8$  

•  $g\left(x\right)=2^x-8$  

The parent function  $f\left(x\right)=3^x$   is shown in red and is translated. What is the equation of the green graph?

•  $g\left(x\right)=3^x+2$  

•  $g\left(x\right)=3^x-2$  

•  $g\left(x\right)=3^{x-2}$  

•  $g\left(x\right)=3^{x+2}$  

The parent function $f\left(x\right)=3^x$ is shown in red and is translated. What is the equation of the green graph?

• $g\left(x\right)=3^x+5$

• $g\left(x\right)=3^x-5$

• $g\left(x\right)=3^{x-5}$

• $g\left(x\right)=3^{x+5}$