Characteristics of Exponential and Logarithmic Functions

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)

Fill in the Blank

Exponential functions have a ________ asymptote.

Fill in the Blank

Logarithmic functions have a _________ asymptote.

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?

• 
  

  $$y=\frac{1}{12}$$  

• $$x=12$$  

• $$x=5$$

• $$y=5$$

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

Notice how our domain and range coincide with end behavior?

Open Ended

How can end behavior help us find the domain and range of the function?

Multiple Choice

Choose the correct choice for end behavior.

• 
  

  $$as\ \left(x\rightarrow-\infty\right),\ \left(y\rightarrow0\right);\ as\ \left(x\rightarrow\infty\right),\left(\ y\rightarrow\infty\right)$$
  

• $$as\ \left[x\rightarrow0\right],\ \left[y\rightarrow-\infty\right];\ as\ \left[x\rightarrow\infty\right],\ \left[y\rightarrow\infty\right]$$

• $$as\ \left[x\rightarrow0,\ y\rightarrow0\right];\ and\ as\ \left[x\rightarrow\infty,\ y\rightarrow\infty\right]$$

Multiple Choice

Whats the horizontal asymptote?

• y=1
• y=0
• (0,-1)
• y=-1

Multiple Choice

What is the y-intercept of the function?

• (0,2)

• (2,0)

• (0,-2)

• (-2,0)

Multiple Choice

Whats the horizontal asymptote?

• (0,3)
• y=3
• y=-2
• y=2

Multiple Choice

What is the range of the function shown below?

• 0 < y < 12
• -2 < y < 5
• y > 0
• All Real Numbers 

Multiple Choice

What is the range?

• (-∞, ∞)
• (0, ∞)
• [1, ∞)
• (1, ∞)

Multiple Choice

What is the domain?

• (-∞, ∞)
• (0, ∞)
• [1, ∞)
• (1, ∞)

Multiple Choice

What is the domain and range of the function y=2^x ?
Use the graph to help!

•  Domain: −∞<x<∞
  Range: y>0
• Domain: −∞<x<∞
  Range: y>1
• Domain: −2<x<∞
  Range: y>0
• Domain: −∞<x<∞
  Range: y>0

Multiple Choice

Where is the asymptote?

• x = 1
• y = 1
• x = -1
• y = -1

Multiple Choice

What is the x-intercept of log₇(x)?

• (2, 0)

• (-1, 0)

• (0, 1)

• (1, 0)

Multiple Choice

Multiple Choice

What is the domain and range of the function y=2^x ?
Use the graph to help!

•  Domain: All Real Numbers
  Range: y>0
• Domain: All Real Numbers
  Range: y>1
• Domain: −2<x<∞
  Range: y>0
• Domain: −∞<x<∞
  Range: y>0

Multiple Choice

What is the Range?

• y > 0
• All Real Numbers
• y > 1
• y < 1

Multiple Choice

What is the range of this graph?

• All Real Numbers
• y > 1
• y > -1
• y > 5

Multiple Choice

What is the domain and range of the function y=2^x ?

Use the graph to help!

• Domain: −∞<x<∞

  Range: y>0

• Domain: −∞<x<∞

  Range: y>1

• Domain: −2<x<∞

  Range: y>0

• Domain: −∞<x<∞

  Range: y<0

Multiple Choice

What is the domain?

• All real numbers

• x > 0

• $$x\ge1$$

• x > 1

Multiple Choice

What is the domain and range of the logarithmic graph ?

• $$D\ :\ -3<x<\infty\ \ \ \ \ \ \ \ \ R\ :\ \ y\ >\ -\infty$$

• $$D\ :\ -3<x<3\ \ \ \ \ \ \ \ \ \ \ \ \ \ R:\ y\le3$$

• 
  

  $$D\ :\ -\infty\ <x<\infty\$$ $$R:\ y>3$$
  

Multiple Choice

The end!

Please complete the assignment:

"Exponential and Logarithmic Graphs"

Multiple Choice

Annual sales for a clothing store is $270,000 and are increasing at a rate of 7% per year. What will the sales amount be after three years?

• $250, 341.51

• $330,761.61

• $126,201.10