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mojhsa [17]
3 years ago
13

Consider the following equation f(x)=(x^2+4)/(4x^2-4x-8)

Mathematics
2 answers:
nadya68 [22]3 years ago
8 0

Answer: x=-1 and x=2 because (this is where the function is undefined) name of horizontal asymptote (y=1/4) because (m=n)

Step-by-step explanation: on edge

kifflom [539]3 years ago
3 0

<em><u>Question:</u></em>

Consider the following equation: f(x)=x^2+4\4x^2-4x-8 name the vertical asymptote(s)

<em><u>Answer:</u></em>

The vertical asymptotes are x = 2 or x = -1

<em><u>Solution:</u></em>

Given that,

f(x)=\frac{x^2+4}{4x^2-4x-8}

For vertical asymptotes, set the denominator to zero and then solve the quadratic equation

4x^2-4x-8=0\\\\Divide\ by\ 2\\\\x^2 - 2x - 4 = 0

Split\ the\ middle\ term\\\\x^2+x-2x-2=0\\\\Group\ the\ equation\\\\(x^2 + x) - (2x + 2) = 0\\\\Factor\ the\ common\ term\\\\x(x + 1) - 2(x + 1) = 0\\\\(x + 1)(x - 2) = 0\\\\Therefore,\\\\x + 1 = 0\\\\x = -1\\\\And\\\\x - 2 = 0\\\\x = 2

Thus the vertical asymptotes are x = - 1 and x = 2

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