Answer
(a) $y=2x+3$
(b) $-2, \frac{3}{2}$
(c) $6$
(d) $x=1$
(e) see graph
Work Step by Step
Given $f(x)=\frac{2x^2+x-6}{x-1}$:
(a) use synthetic division as shown, we have $f(x)=\frac{2x^2+x-6}{x-1}=2x+3-\frac{3}{x-1}$, thus the oblique asymptote is $y=2x+3$
(b) X-intercept: $f(x)=0\longrightarrow (x+2)(2x-3)=0\longrightarrow x=-2, \frac{3}{2}$
(c) Y-intercept: $f(0)=6$
(d) Vertical asymptote: $x=1$
(e) Use test points as necessary to graph the function as shown.