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Unformatted text preview: COLLEGE ALGEBRA NAME: ________________________________ GPS # 38 Class Time: ____________ Date: __________ 4.5 RATIONAL FUNCTIONS AND RATIONAL EQUATIONS II Useful Guidelines:
To analyze the graph of a rational function, R( x) = p( x)
, in lowest terms:
q( x) * Step 1:
* Step 2:
* Step 3:
* Step 4:
* Step 5: Find the domain of the rational function.
Find the x-intercept(s), if any (let p ( x) = 0 when R( x) is in lowest term), and the y-intercept(s), R(0) .
Write R in lowest term and find the real zeros of the denominator (vertical asymptotes).
Find the horizontal or slant asymptotes, if any.
Find the intervals on which R is above the x-axis and the intervals on which R is below the x-axis.
[Hint: pick a point between the zeros obtained from both the numerator and the denominator.]
* Step 6: Graph the asymptotes, if any, plot the points, connect the points and graph R.
Analyze the graph of each function by following Step 1 through 6 above.
2 x ! 10
R( x) =
x 2) Rev. S08 R( x) = x 2 ! 25
x!5 http://faculty.valenciacc.edu/ashaw/ ...
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