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Let Find the values of k for which the equation x=k is a vertical asymptote of the graph of y=f(x). Enter all such values, separated by commas.

 Apr 18, 2020
 #1
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Factor both the numerator and the denominator:

                  f(x)  =  [ 2(x + 5)(x - 5) ] / [ (x + 5)(x - 3) ]

 

Since the factor (x + 5 ) is found in both the numerator and the denominator, it produces a hole in the function at x = -5.

 

Cancelling out that term, we have:  f(x)  =  [ 2(x - 5) ] / [ (x - 3) ]

There will be a vertical asymptote at x = 3 (because it makes the denominator zero).

 Apr 18, 2020

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