which graph is the graph of $f(x)=\frac{x - 1}{x + 2}$?

Explanation:

Step1: Find the vertical asymptote

Set the denominator equal to zero. $x + 2=0$, so $x=-2$.

Step2: Find the horizontal asymptote

Since the degrees of the numerator and denominator are the same (both degree 1), the horizontal asymptote is $y=\frac{1}{1}=1$ (the ratio of the leading - coefficients).

Step3: Find the x - intercept

Set $y = 0$, then $\frac{x - 1}{x + 2}=0$, so $x-1 = 0$ and $x = 1$.

Step4: Find the y - intercept

Set $x = 0$, then $y=\frac{0 - 1}{0+2}=-\frac{1}{2}$.

Based on the vertical asymptote $x=-2$, horizontal asymptote $y = 1$, x - intercept at $x = 1$ and y - intercept at $y=-\frac{1}{2}$, you can identify the correct graph among the options.

(Without the actual option - naming, we can't give a specific letter - answer. But the above steps help in graph - identification).