Asymptotes - Algebra II
Card 0 of 7
What is the horizontal asymptote of the graph of the equation 
?
What is the horizontal asymptote of the graph of the equation
The asymptote of this equation can be found by observing that 
regardless of 
. We are thus solving for the value of 
as 
approaches zero.
So the value that 
cannot exceed is 
, and the line 
is the asymptote.
The asymptote of this equation can be found by observing that
So the value that
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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
An exponential equation of the form 
has only one asymptote - a horizontal one at 
. In the given function, 
, so its one and only asymptote is 
.
An exponential equation of the form
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Find the vertical asymptote of the equation.
Find the vertical asymptote of the equation.
To find the vertical asymptotes, we set the denominator of the function equal to zero and solve.
To find the vertical asymptotes, we set the denominator of the function equal to zero and solve.
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Consider the exponential function 
. Determine if there are any asymptotes and where they lie on the graph.
Consider the exponential function
For positive 
values, 
increases exponentially in the 
direction and goes to positive infinity, so there is no asymptote on the positive 
-axis. For negative 
values, as 
decreases, the term 
becomes closer and closer to zero so 
approaches 
as we move along the negative 
axis. As the graph below shows, this is forms a horizontal asymptote.
For positive
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Determine the asymptotes, if any: 
Determine the asymptotes, if any:
Factorize both the numerator and denominator.
Notice that one of the binomials will cancel.
The domain of this equation cannot include 
.
The simplified equation is:
Since the 
term canceled, the 
term will have a hole instead of an asymptote.
Set the denominator equal to zero.
Subtract one from both sides.
There will be an asymptote at only: 
The answer is: 
Factorize both the numerator and denominator.
Notice that one of the binomials will cancel.
The domain of this equation cannot include
The simplified equation is:
Since the
Set the denominator equal to zero.
Subtract one from both sides.
There will be an asymptote at only:
The answer is:
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Which of the choices represents asymptote(s), if any? 
Which of the choices represents asymptote(s), if any?
Factor the numerator and denominator.
Notice that the 
terms will cancel. The hole will be located at 
because this is a removable discontinuity.
The denominator cannot be equal to zero. Set the denominator to find the location where the x-variable cannot exist.
The asymptote is located at 
.
Factor the numerator and denominator.
Notice that the
The denominator cannot be equal to zero. Set the denominator to find the location where the x-variable cannot exist.
The asymptote is located at
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Where is an asymptote located, if any? 
Where is an asymptote located, if any?
Factor the numerator and denominator.
Rewrite the equation.
Notice that the 
will cancel. This means that the root of 
will be a hole instead of an asymptote.
Set the denominator equal to zero and solve for x.
An asymptote is located at: 
The answer is: 
Factor the numerator and denominator.
Rewrite the equation.
Notice that the
Set the denominator equal to zero and solve for x.
An asymptote is located at:
The answer is:
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