Consider the following hx 2x2x 3 a State the domain of the

Consider the following. h(x) = 2/x^2(x - 3) (a) State the domain of the function. all real numbers x except x = 9 all real numbers x except x = -3 all real numbers x except x = 2 all real numbers x all real numbers x except x = 0 and x = 3 (b) Identify all intercepts. (If an answer does not exist, enter ONE.) x-intercept (x, y) = () y-intercept (x, y) = () (c) Find any vertical and horizontal asymptotes. (Enter you- answers as a comma-separated list of equations. If there are no asymptotes, enter DNE.) Plot additional solution points as needed to sketch the rational function.

Solution

a)
At x=0 and x = 3, h(x) will be undefined
So,
domain is all real number except x=0 and x=3

b)
for x intercept, put h(x) = 0
0 = 2/(x^2 (x-3))
it can\'t be solved, so DNE

for y intercept, put x= 0
y = 2/0 = undefined
So,
DNE
Answer:
DNE
DNE

c)
vertical asymptodes, when h(x) = infinity
That is at x = 0 and x=3

Since degree of denominator is more, horizontal asymptodes is
y= 0

d)
correct graph is the 1st graph