$\"\"$

The logarithm expression is $\"\"$ .

Change of base formula : $\"\"$ .

$\"\"$

Construct a table of values to find ordered pairs that satisfy the function :

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$

Graph :

(1) Draw the coordinate plane.

(2) Plot the points from the table of values.

(3) Connect the plotted points to a smooth curve.

$\"\"$

Observe the above graph :

Domain of the function is $\"\"$ .

Range of the function is $\"\"$ .

Find $\"\"$ -intercept by substituting $\"\"$ in $\"\"$ .

$\"\"$

Apply definition of logarithm : $\"\"$ if and only if $\"\"$ .

$\"\"$

$\"\"$ -intercept is $\"\"$ .

Find $\"\"$ -intercept by substituting $\"\"$ in $\"\"$ .

$\"\"$

Since $\"\"$ is not in the domain of logarithm $\"\"$ -intercept does not exist.

Find the horizontal and vertical asymptotes.

Observe the above graph the function does not have horizontal asymptote.

The equation of vertical asymptote of graph of the function $\"\"$ is $\"\"$ .

Thus the vertical asymptote of graph function $\"\"$ is $\"\"$ .

End behavior : $\"\"$ and $\"\"$ .

The function is increasing over the interval $\"\"$ .

$\"\"$

Graph of the function $\"\"$ is

$\"\"$

Domain of the function is $\"\"$ .

Range of the function is $\"\"$ .

$\"\"$ -intercept is $\"\"$ .

$\"\"$ -intercept does not exist.

There is no horizontal asymptote.

The vertical asymptote of the function $\"\"$ is $\"\"$ .

End behavior : $\"\"$ and $\"\"$ .

The function is increasing over the interval $\"\"$ .