Question

which is the graph of $y = \frac{2}{x + 1} - 6$? (with a graph showing a coordinate plane and a blue curve, and multiple choice options)

Explanation:

Step1: Analyze the vertical asymptote

For a rational function \(y=\frac{2}{x + 1}-8\), the vertical asymptote occurs when the denominator is zero. Set \(x+1 = 0\), then \(x=-1\).

Step2: Analyze the horizontal asymptote

For the function \(y=\frac{2}{x + 1}-8\), as \(x
ightarrow\pm\infty\), \(\frac{2}{x + 1}
ightarrow0\). So the horizontal asymptote is \(y=-8\).

Answer:

The graph of \(y = \frac{2}{x+1}-8\) has a vertical asymptote at \(x=-1\) and a horizontal asymptote at \(y = -8\).