QuestionRewrite $f(x)$ in factored form, but do not simplify: $$f(x)=\frac{4 x^{2}-9 x+2}{5 x^{2}+21 x+4}=$$ $\square$ x -Intercepts Write intercepts as $(x, y)$ points: $\square$ y-Intercepts Write intercepts as $(x, y)$ points: $\square$ Vertical Asymptotes $$x=\square$$
Horizontal Asymptotes $$y=\frac{4}{5} \quad$$
Oblique Asymptotes $$y=\text { DNE } \quad \checkmark$$ $\square$ $\sigma^{\infty}$ Question Help: Video

Studdy Solution
Confirm horizontal and oblique asymptotes.
Since the degrees of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients:
$$y = \frac{4}{5}$$
There is no oblique asymptote because the degrees of the numerator and denominator are equal.
The factored form of $f(x)$ is:
$$f(x) = \frac{(4x - 1)(x - 2)}{(5x + 1)(x + 4)}$$
x-intercepts: $(\frac{1}{4}, 0)$, $(2, 0)$
y-intercept: $(0, \frac{1}{2})$
Vertical asymptotes: $x = -\frac{1}{5}$, $x = -4$
Horizontal asymptote: $y = \frac{4}{5}$
Oblique asymptote: DNE