Question

determine the function which corresponds to the given graph.
The asymptote is x=-3

Answer 1

we are given

vertical asymptote at x=-3

so, there will be x+3 in the denominator

we are given zeros at x=-2

so, there will x+2 in the numerator

so, we can set up function as

$f(x)=\frac{a(x+2)}{(x+3)}$

we can select any one point

and then we can find 'a'

(0,1)

so, we can plug f(x)=1 and x=0

and find 'a'

$1=\frac{a(0+2)}{(0+3)}$

$a=\frac{3}{2}$

now, we can plug back

and we get

$f(x)=\frac{\frac{3}{2}(x+2)}{(x+3)}$..............Answer