Question

what is the vertical asymptotes? y = \frac{x + 5}{x - 6} x = -5 x = -6 x = 5 x = 6

Explanation:

Step1: Recall the definition of vertical asymptotes

For a rational function \(y=\frac{f(x)}{g(x)}\), vertical asymptotes occur at \(x = a\) where \(g(a)=0\) and \(f(a)
eq0\).

Step2: Set the denominator equal to zero

Given \(y=\frac{x + 5}{x-6}\), set \(x-6=0\).
$$x-6=0$$

Step3: Solve for \(x\)

Add \(6\) to both sides of the equation \(x-6 = 0\).
$$x=6$$

Step4: Check the numerator at \(x = 6\)

Substitute \(x = 6\) into the numerator \(x + 5\): \(6+5=11
eq0\).

So the vertical asymptote is \(x = 6\).

Answer:

D. \(x = 6\)