Question

Determine the function which corresponds to the given graph
The asymptote is x=3

Answer 1

The function has a horizontal asymptote at y = 3.
The function has a vertical asymptote at x = -3.
The function has a vertical intercept of 1.
The function has a zero of x = -2.

Because the function has a zero at x = -2, and a vertical asymptote at x = -3, therefore

`y= (k(x+2))/(x+3)`

Write the function in the form
y =
`y= (k(1+ (2)/(x)) )/(1+ (3)/(x) )`

As x → ∞, y → k.
Because a horizontal asymptote exists at y = 3, therefore k = 3.
A vertical intercept exists at y = 1.
The function is

`y = (3(x+2)(x+1))/((x+3)(x+1))`

Answer:
`y = (3(x+2)(x+1))/((x+3)(x+1))`