Question$$f(x)=\frac{-2 x^{2}-10 x-8}{x^{2}+x-2}$$
Graph the following key features of $f(x)$ : 1) $y$-intercept(s) 2) $x$-intercept(s) 3) vertical asymptote(s) 4) horizontal asymptote(s)

Studdy Solution
To determine the horizontal asymptote, compare the degrees of the numerator and the denominator:
Both the numerator and the denominator are degree 2 polynomials. The horizontal asymptote is given by the ratio of the leading coefficients:
$$y = \frac{-2}{1} = -2$$
The horizontal asymptote is $y = -2$.
The key features of the graph of $f(x)$ are: 1) $y$-intercept: $(0, 4)$ 2) $x$-intercepts: $(-4, 0)$ and $(-1, 0)$ 3) Vertical asymptotes: $x = -2$ and $x = 1$ 4) Horizontal asymptote: $y = -2$