Algebra II : Graphing Logarithmic Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Graphing Logarithmic Functions

Give the -intercept of the graph of the function

to two decimal places.

Possible Answers:

The graph has no -intercept.

Correct answer:

Explanation:

Set  and solve:

The -intercept is .

Example Question #2 : Graphing Logarithmic Functions

Give the  intercept of the graph of the function

to two decimal places.

Possible Answers:

The graph has no -intercept.

Correct answer:

Explanation:

Set  and solve:

The -intercept is .

Example Question #3 : Graphing Logarithmic Functions

What is/are the asymptote(s) of the graph of the function  ?

Possible Answers:

 and 

 and 

Correct answer:

Explanation:

The graph of the logarithmic function

has as its only asymptote the vertical line 

Here, since , the only asymptote is the line

.

Example Question #4 : Graphing Logarithmic Functions

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Use the change of base formula for the logarithmic function.

Or

 can be solved using .

 

Example Question #5 : Graphing Logarithmic Functions

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Use the change of base formula for logarthmic functions.

Or

 can be solved using 

Example Question #6 : Graphing Logarithmic Functions

Solve for 

Possible Answers:

No real solutions

Correct answer:

Explanation:

Use the change of base formula for logarithmic functions and incorporate the fact that  and 

Or

 can be solved using 

Example Question #7 : Graphing Logarithmic Functions

Solve for 

Possible Answers:

Correct answer:

Explanation:

Use the change of base formula for logarithmic functions to solve this problem.

Or

 can be solved using 

For this specific problem we need to remember that  gives an unreal number therefore is not our answer. 

Thus,

.

Example Question #8 : Graphing Logarithmic Functions

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Use the change of base formula for logarithmic functions.

Or

 can be solved using 

Example Question #9 : Graphing Logarithmic Functions

Solve for 

Possible Answers:

Correct answer:

Explanation:

Use the change of base formula for logarithmic functions.

Or

 can be solved using 

Example Question #10 : Graphing Logarithmic Functions

Which is true about the graph of 

 ?

Possible Answers:

When  ,  is twice the size as in the equation 

All of the answers are correct

The range of the function is infinite in both directions positive and negative.

The domain of the function is greater than zero

None of the answers are correct

Correct answer:

All of the answers are correct

Explanation:

There is no real number  for which 

Therefore in the equation  ,  cannot be 

However,  can be infinitely large or negative.

Finally, when   or twice as large.

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