SOLUTION: Graph the rational function f(x)= X^2+4X+3/2X+4

Question 1136720: Graph the rational function f(x)= X^2+4X+3/2X+4
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

I will assume you mean

and not

If you are working a problem like this, you should know that parentheses are required....

(1) y-intercept: set x=0 --> 3/4

(2) x-intercepts: where the function value is 0 -- i.e., where the numerator is 0.

so x-intercepts at -3 and -1

(3) horizontal asymptote: none (the degree of the numerator is 1 more than the degree of the denominator; the function has a (linear) oblique asymptote.

(4) vertical asymptote: where the denominator is 0 -- at x=-2.

Perform polynomial division to find the oblique asymptote:

The oblique asymptote is y = (1/2)x+1.

A graph of the function and the oblique asymptote:

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