# Algebra II : Solving and Graphing Logarithms

## Example Questions

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### 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 #1 : Graphing Logarithmic Functions

Which is true about the graph of ?

When , is twice the size as in the equation The range of the function is infinite in both directions positive and negative.

The domain of the function is greater than zero

All of the answers are correct

None of the answers are correct

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 .      Explanation:

Let . In terms of , .

The graph of has as its vertical asymptote the line of the equation . The graph of is the result of three transformations on the graph of - a left shift of 4 units , a vertical stretch ( ), and an upward shift of 2 units ( ). Of the three transformations, only the left shift affects the position of the vertical asymptote - the asymptote of also shifts left 4 units, to .

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