Graphing Transformed Exponential Functions

Check all functions that represent exponential growth.

• $f\left(x\right)=\left(2\right)^x$

• $f\left(x\right)=\left(\frac{1}{2}\right)^x$

• $f\left(x\right)=-\left(5\right)^x$

• $f\left(x\right)=\left(\frac{7}{2}\right)^x$

Which function has an "h" value of 3?

• $f\left(x\right)=\left(2\right)^{x+3}-4$

• $f\left(x\right)=\left(3\right)^{x+2}-4$

• $f\left(x\right)=\left(2\right)^{x-3}-4$

• $f\left(x\right)=\left(2\right)^{x+4}+3$

 $f\left(x\right)=-2\left(3\right)^{x+1}-7$  Determine the correct values of a, h, and k. 

• a=-2, h=1, k=-7

• a=-2, h=-1, k=-7

• a=2, h=1, k=7

• a=3, h=-2, k=1

 $f\left(x\right)=\left(\frac{1}{2}\right)^{x+6}-1$  

What is the horizontal asymptote?

• y = -1

• y = 6

• x = -1

• y = -6

 $f\left(x\right)=-2\left(\frac{1}{3}\right)^{x-1}+5$  Describe the transformations for the function.

• Reflect over x-axis, shift left 1, shift up 5.

• Reflect over x-axis, vertical stretch, shift left 1, shift up 5.

• Vertical compression, shift right 1, shift up 5.

• Reflect over x-axis, vertical stretch, shift right 1, shift up 5.

Which of the following functions has been translated 2 units to the left and 6 units down?

• $f\left(x\right)=\left(4\right)^{x+2}-6$

• $f\left(x\right)=\left(2\right)^{x-4}-6$

• $f\left(x\right)=\left(4\right)^{x-2}-6$

• $f\left(x\right)=\left(2\right)^{x+4}-6$

Which of the following functions has a vertical compression?

• $f\left(x\right)=\left(\frac{1}{4}\right)^{x-5}$

• $f\left(x\right)=\frac{1}{4}\left(3\right)^{x-5}$

• $f\left(x\right)=-\left(4\right)^{x+5}$

• $f\left(x\right)=-\left(\frac{1}{4}\right)^{x+5}$

 $f\left(x\right)=4\left(\frac{1}{4}\right)^{x+8}-3$  

What is the parent function?

•  $f\left(x\right)=\left(4\right)^x$  

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

•  $f\left(x\right)=\left(\frac{1}{4}\right)^x$  

•  $f\left(x\right)=4\left(\frac{1}{4}\right)^x$  

 $f\left(x\right)=-\left(2\right)^{x+1}+4$  

Determine the correct graph for the function.

• 
• 
• 
• 

What is the domain for the following graph?

• $\left(-\infty,\ \infty\right)$

• $\left(\infty,-\infty\right)$

• $\left(4,\ \infty\right)$

• $\left(-\infty,\ 4\right)$