Parametric Equation: Rational Function
General Contents
Detailed Contents
Index
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If you want to see all of the following steps at once, click the "All Steps" button. Otherwise, use the "Next" button.
Solve and graph
.
Are there any restrictions on the values of
t
?
Yes
What are they?
Because of (
t
– 2) in the denominator,
we must exclude
t
= 2.
What about values like 1.99 or 2.01?
They result in small values of the denominator of the
y
equation.
What will the corresponding value of
y
be?
y
will be large.
Use a graphing calculator to plot this function. Then confirm by clicking the “Next” button.
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Let’s determine the rectangular equation of this curve. How do we do that?
We can solve the
x
equation for
t
.
Do that.
We get
Substitute this result into the “
y
” equation.
We get
.
What type of function is this?
A
rational function
.
How do we find the horizontal asymptote?
By taking the limit as
x
approaches positive or negative infinity.
Do that.
We get
y
= 2.
Does this agree with the graph?
Yes, the curve seems to approach
y
= 2 for large positive or negative values of
x
.
How do we find the vertical asymptote?
We determine where the denominator approaches 0.
Do that.
In this case, that is at
x
= 0.
Does this agree with the graph?
Yes.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
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General Contents
Detailed Contents
Index