# Algebra II : Graphing Logarithmic Functions

## Example Questions

### Example Question #1 : Graphing Logarithmic Functions

Give the -intercept of the graph of the function

to two decimal places.

The graph has no -intercept.

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.

The graph has no -intercept.

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  ?

and

and

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

Which is true about the graph of

?

All of the answers are correct

The domain of the function is greater than zero

When  ,  is twice the size as in the equation

None of the answers are correct

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

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.

### Example Question #5 : Graphing Logarithmic Functions

Which of the following is true about the graph of

It is an odd function.

It is an even function.

The range must be greater than zero.

The domain is infinite in both directions.

The graph is the mirror image of  flipped over the line

The graph is the mirror image of  flipped over the line

Explanation:

is the inverse of  and therefore the graph is simply the mirror image flipped over the line

### Example Question #6 : Graphing Logarithmic Functions

Give the equation of the horizontal asymptote of the graph of the equation

.

The graph of  does not have a horizontal asymptote.

The graph of  does not have a horizontal asymptote.

Explanation:

Let

In terms of ,

This is the graph of  shifted left 4 units, stretched vertically by a factor of 3, then shifted up 2 units.

The graph of  does not have a horizontal asymptote; therefore, a transformation of this graph, such as that of , does not have a horizontal asymptote either.

### Example Question #7 : Graphing Logarithmic Functions

Find the equation of the vertical asymptote of the graph of the equation

.