### All Algebra II Resources

## Example Questions

### 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:**

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:**

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:**

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:**

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:**

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:**

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:**

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:**

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:**

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

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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