Explain why the function f (x) = 5x-15/x-3 is not asymptotic to the line x=3. sketch the graph of this function.

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Yosef Hayes

Mathematics

6 July, 11:31

Explain why the function f (x) = 5x-15/x-3 is not asymptotic to the line x=3. sketch the graph of this function.

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Salvatore · Answer 1

X=3 is a vertical line. The question is "Is this line a vertical asymptotefor the function f (x) ?". Vertical asymptote is vertical line near which the function grows without bound.

The function f (x) = 5x-15/x-3 is not asymptotic to the line x=3, because for x=3 f (x) = 5*3-15/3-3=0/0=0. So, there is a value for x=3 and the function f (x) does not grow near x=3 without bound.