12. Find the vertical and horizontal asymptotes and any holes (if they exist) in the graphs of the following rational functions. If there is a hole, state the ordered pair where it exists. a) f(x) = (x-8)/(x-7) Vertical asymptote: Horizontal asymptote: Hole: b) g(x) = (x^2-3x-10)/(x+5) Vertical asymptote: Horizontal asymptote: Hole: c) h(x) = (x^2-25) Vertical asymptote: Horizontal asymptote: Hole:
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There is no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator. There is a hole at $x=-4$ because the factor $(x+4)$ cancels out. Show more…
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