SOLUTION: What function has the following characteristics? A zero at x = 4 and at x = -2 A y-intercept at y = 16/3 A vertical asymptote at x = 3 A slant asymptote at y = 2x + 2

Question 1158027: What function has the following characteristics?
A zero at x = 4 and at x = -2
A y-intercept at y = 16/3
A vertical asymptote at x = 3
A slant asymptote at y = 2x + 2
Answer by KMST(5385) (Show Source): You can put this solution on YOUR website!
Condition #1: A zero at x = 4 and at x = -2
How to satisfy it: include(x-4) and (x+2) as factors

Condition #2: A y-intercept at y = 16/3
How to satisfy it: after satisfying other conditions, add a constant factor K to satisfy

Condition #3: A vertical asymptote at x = 3
How to satisfy it: include (x-3) as a denominator

Tentative solution to satisfy all 3 conditions above:

to satisfy , we make -->

So far, the function we have is , and its graph looks like this:

Condition #4: A slant asymptote at
We need

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