To determine the vertical asymptote(s) of the following function, $$f(x) = \frac{x}{x^2+3x-4}$$, the first step would be to: Evaluate the limits. Factor the denominator. Set the numerator equal to zero and solve. Set x equal to zero and evaluate.
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x^2 + 3x - 4 = (x + 4)(x - 1). Show more…
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To find the vertical asymptotes, we look for values for which the function becomes unbounded. This means for the given function. We should find where the denominator equals 0. We therefore equate the denominator to 0 and factor. Solving gives x = -1/6 (smaller value) and x = 0 (larger value). Part 2: To check the numerator at these values, we evaluate the numerator. The numerator does not become unbounded. We therefore conclude that both x = -1/6 and x = 0 are vertical asymptotes.
Adi S.
Determine the vertical asymptotes of the graph of the function. $$f(x)=\frac{3-x}{(x-4)(x+6)}$$
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