Analyzing Exponential Functions w./ Transformations

Analyzing Exponential Functions w./ Transformations

Week 25: Wednesday, 3/3

Multiple Choice

What is the domain of this exponential function?

 $f\left(x\right)=3^x-2$  

•  $\left(-\infty,0\right)$  

•  $\left(0,\infty\right)$  

• All Real Numbers

• The domain does not exist.

Multiple Choice

What is the range of this function?

 $f\left(x\right)=2\cdot4^x+6$  

•  $x>0$  

•  $x>6$  

•  $y>0$  

•  $y>6$  

Multiple Choice

What is the asymptote of this function?

 $f\left(x\right)=2\cdot4^x+6$  

•  $x=0$  

•  $x=6$  

•  $y=0$  

•  $y=6$  

Multiple Choice

What is the y-intercept of this function? (Hint: Use Desmos!)

 $f\left(x\right)=5^{\left(x-2\right)}+4$  

• (0, 4.04)

• (0, 0)

• (0, 1)

• (4.04, 0)

Multiple Choice

What is the end behavior  of this function? (Hint: Use Desmos!)

 $f\left(x\right)=5\cdot3^x+7$  

• As x goes left, y goes towards 7. 
  
  As x goes right, y goes up.

• As x goes left, y goes up. 
  
  
  As x goes right, y goes towards 7.

Multiple Choice

What is the domain of this exponential function?

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

•  $\left(-\infty,0\right)$  

•  $\left(0,\infty\right)$  

• All Real Numbers

• The domain does not exist.

Multiple Choice

What is the range of this function?

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

•  $x>0$  

•  $x>3$  

•  $y>0$  

•  $y>3$  

Multiple Choice

What is the asymptote of this function?

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

•  $x=0$  

•  $x=3$  

•  $y=0$  

•  $y=3$  

Multiple Choice

What is the y-intercept of this function? (Hint: Use Desmos!)

 $f\left(x\right)=2^x-3$  

• (0, 1)

• (0, 0)

• (1.585, 0)

• (0, -2)

Multiple Choice

What is the end behavior  of this function? (Hint: Use Desmos!)

 $f\left(x\right)=\left(\frac{1}{2}\right)\cdot5^{\left(x-3\right)}+2$  

• As x goes left, y goes towards 2. 
  
  As x goes right, y goes up.

• As x goes left, y goes up. 
  
  
  As x goes right, y goes towards 2.

Multiple Select

How does this function transform?

 $f\left(x\right)=2\cdot3^x+2$  

• Moves Up

• Moves Down

• Moves Left

• Moves Right

• Stretches

Multiple Select

How does this function transform?

 $f\left(x\right)=\frac{1}{3}\cdot5^{\left(x-2\right)}-5$  

• Moves Up

• Moves Down

• Moves Left

• Moves Right

• Compresses

Multiple Select

How does this function transform?

 $f\left(x\right)=5^{\left(x+3\right)}-7$  

• Moves Up

• Moves Down

• Moves Left

• Moves Right

• Stretches