R(x)=x^2+x-6/x-3 what is the domain, intercepts, vertical asymptote, and forming interval. Show work

Question

Analyze the graph of the following function

R(x)=x^2+x-6/x-3

the domain

Find intercepts

Vertical asymptote

divided by

forming interval

graph

Answer 1

R(x)=(x²+x-6)/(x+3)=(x+3)(x-2)/(x+3)=x-2 if x≠-3.

R(x) behaves like the linear function f(x)=x-2 (a straight line with y-intercept=-2 and x-intercept x=2). But R(x) is strictly undefined at x=-3 (there's a hole at (-3,-5)). The hole limits the domain (x values) so the domain can be expressed as {(-∞,-3) (-3,∞)}.

There is no vertical asymptote, but there is a hole.