Graphing Logarithmic Functions - Algebra II
Card 0 of 7
Give the 
intercept of the graph of the function
to two decimal places.
Give the
to two decimal places.
Set 
and solve:
The 
-intercept is 
.
Set
The
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Give the 
-intercept of the graph of the function
to two decimal places.
Give the
to two decimal places.
Set 
and solve:
The 
-intercept is 
.
Set
The
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What is/are the asymptote(s) of the graph of the function 
?
What is/are the asymptote(s) of the graph of the function
The graph of the logarithmic function
has as its only asymptote the vertical line
Here, since 
, the only asymptote is the line
.
The graph of the logarithmic function
has as its only asymptote the vertical line
Here, since
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Which is true about the graph of
?
Which is true about the graph of
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.
There is no real number
Therefore in the equation
However,
Finally, when
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Which of the following is true about the graph of
Which of the following is true about the graph of
is the inverse of 
and therefore the graph is simply the mirror image flipped over the line 
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Find the equation of the vertical asymptote of the graph of the equation
.
Find the equation of the vertical asymptote of the graph of the equation
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 
.
Let
The graph of
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Give the equation of the horizontal asymptote of the graph of the equation
.
Give the equation of the horizontal asymptote of the graph of the equation
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.
Let
In terms of
This is the graph of
The graph of
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