Find the vertical asymptotes, if any, for the following function. f(x)=x+8/x^2-100

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Find the vertical asymptotes for `f(x)=(x+8)/(x^2-100)` .

Note that vertical asymptotes occur when a function with no common factors in the numerator and denominator has a factor that causes a division by zero.

Rewrite f(x) as `f(x)=(x+8)/((x+10)(x-10))` . There are no common factors in the numerator and denominator.

Therefore there are vertical asymptotes at x=-10 and x=10.

The graph:

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