domain:
v. a:
roots:
y-int:
h. a:
holes:
o. a:

also, draw on the graph.

See below.

Step-by-step explanation:

Domain is All Real x ;  where x ≠ -2 , x ≠ 1.

Vertical asymptotes: x = -2 and x = 1.

Roots are the solution of (2x + 3)(x - 6) = 0. That is {-1.5, 6}.

Y-intercept  is the value of y when x = 0:

= 2(0) + 3)(0 - 6) / ( 0 + 2)( 0 - 1)

= -18/-2 =  9. So it's (0, 9).

Horizontal asymptotes:

The limit of the function as x approaches infinity:

The terms in x^2 are 2x^2 in the numerator and x^2 in the denominator so the limit is +2.

There is an asymptote y = 2.

Holes:

No factors cancel out so there are no holes.

I'm not sure about O.A.

a) false; the points do not have to be in a straight line.

step-by-step explanation:

the points could be in the shape of a triangle

b is incorrect

c is incorrect because it is saying the immediately don't form one when they are capable of doing so

d is incorrect

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3