Question

write an equation for the function graphed below y =

Explanation:

Step1: Determine the form of the rational function

The vertical asymptotes are \(x = - 2\) and \(x = 4\), so the denominator is \((x + 2)(x - 4)=x^{2}-2x - 8\). The \(x\) - intercept is \(x = 3\), so the numerator has a factor of \((x - 3)\). Let the function be \(y=\frac{a(x - 3)}{(x + 2)(x - 4)}\).

Step2: Find the value of \(a\)

The \(y\) - intercept is \(y = 2\). When \(x = 0\), we substitute into the function:

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Answer:

\(y=\frac{16(x - 3)}{3(x + 2)(x - 4)}\)