Question

F(x)=2x^2 + x - 6/ x-1

Answer 1

Answer:

See below

Step-by-step explanation:

Zeroes:

$f(x)=\frac{2x^2+x-6}{x-1}$

$0=\frac{2x^2+x-6}{x-1}$

$0=2x^2+x-6$

$0=(2x-3)(x+2)$

$x=\frac{3}{2},-2$

Vertical and Horizontal Asymptotes:

$x\neq 1$ is excluded from the domain, therefore, there's a vertical asymptote at $x=1$

No horizontal asymptotes as the degree of the numerator is greater than the degree of the denominator by 1.

Oblique (Slant) Asymptote:

$f(x)=\frac{2x^2+x-6}{x-1}=2x+3,R(-3)$, so the oblique/slant asymptote is $y=2x+3$