Exponential and Logarithmic

Characteristics of Exponential and Logarithmic Functions

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Vocabulary

• Asymptote: A line that a function approaches

• Domain: The set of all x-values. (Look left and right)

• Range: The set of all y-values (Look down and up)

Multiple Choice

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Multiple Choice

A given exponential function has an asymptote at y=12. What must be the asymptote of the inverse?

• $$y=\frac{1}{12}$$

• $$x=12$$

• $$x=-12$$

• $$y=-12$$

Multiple Choice

A given logarithmic function has an asymptote at x=5. What must be the asymptote of the inverse?

• 
  

  $$x=\frac{1}{5}$$  

• $$y=\frac{1}{5}$$  

• $$x=5$$

• $$y=5$$

Multiple Choice

A given exponential function has an asymptote at y=-1. What must be the asymptote of the inverse?

• $$y=-1$$

• $$x=-1$$

• $$x=1$$

• $$y=1$$

Multiple Choice

An exponential function has a domain of:

$$\left(-\infty,\infty\right)$$  
What is the range of the inverse function?

• $$\left(-\infty,\infty\right)$$  

• $$\left(\infty,-\infty\right)$$  

• Cannot determine from the given information.

Multiple Choice

An exponential function has a range of:

$$\left(3,\infty\right)$$  
What is the domain of the inverse function?

• $$\left(\infty,3\right)$$  

• $$\left(3,\infty\right)$$  

• Cannot determine from the given information.

Multiple Choice

An logarithmic function has a domain of:

$$\left(-1,\infty\right)$$  
What is the domain of the inverse function?

• $$\left(\infty,1\right)$$  

• $$\left(-1,\infty\right)$$  

• Cannot determine from the given information.

Multiple Choice

What is the asymptote of the yellow and green function.

• yellow: y=0

  green: x=0

• yellow: y=1

  green: x=1

• yellow: y=-1

  green: x=-1

• yellow: y=-1

  green: x=1

Multiple Select

What is the domain and range of the green function? (Choose 2)

• Domain:

  $$\left(-1,\infty\right)$$

• Domain:
  $$\left(-\infty,\infty\right)$$
  

• Range: $$\left(-1,\infty\right)$$

• Range: $$\left(-\infty,\infty\right)$$