
The equations and the values of x for any vertical asymptotes and any holes in the graph of the given rational function.

Answer to Problem 9.4.3EP
x=−1 and x=8 are vertical asymptotes of the given rational function.
Explanation of Solution
Given: f(x)=5(x+1)(x−8)
f(x)=5(x+1)(x−8) be the given rational function and it has to find any vertical asymptotes and any holes for the value of x .
Now f(x)=5(x+1)(x−8) is given equation and x+1 and x−8 are its denominator.
For vertical asymptotes x+1=0
x+1=0
x=−1
Here in solution there is no factor that cancels in the numerator.
And x=−1 is the identical factor in the numerator that is vertical asymptote.
For vertical asymptotes x−8=0
x−8=0
x=8
Here in solution there is no factor that cancels in the numerator.
And x=8 is the identical factor in the numerator that is vertical asymptote
Now graph of the function f(x)=5(x+1)(x−8) is
Hence, x=−1 and x=8 are vertical asymptotes of the given rational function.
Chapter EP Solutions
Algebra 2
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