Algebra II : Graphing Exponential Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #4 : Graph Exponential Functions

Does the function  have any -intercepts? 

Possible Answers:

Yes, 

Yes,  and 

Yes, 

That cannot be determined from the information given. 

No 

Correct answer:

No 

Explanation:

The -intercept of a function is where . Thus, we are looking for the -value which makes .

If we try to solve this equation for  we get an error.

To bring the exponent down we will need to take the natural log of both sides.

Since the natural log of zero does not exist, there is no exponent which makes this equation true.

Thus, there is no -intercept for this function. 

Example Question #31 : Solving Exponential Functions

Which of the following correctly describes the graph of an exponential function with a base of three?

Possible Answers:

It stays constant. 

It begins by decreasing quickly and then levels out. 

It begins by decreasing gradually and then decreases more quickly. 

It starts out by gradually increasing and then increases faster and faster. 

It starts by increasing quickly and then levels out. 

Correct answer:

It starts out by gradually increasing and then increases faster and faster. 

Explanation:

Exponential functions with a base greater than one are models of exponential growth. Thus, we know that our function will increase and not decrease. Remembering the graph of an exponential function, we can determine that the graph will begin gradually, almost like a flat line. Then, as  increases,  begins to increase very quickly. 

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