First, the asymptotes. These are prohibited values of x in a denominator, so the denominator must look like (x-4)(x+4)=x²-16.
Next, numerator must contain the factors x-3 and x+5 to establish the x intercepts. If we write the numerator as a(x-3)(x+5), where a is a constant, we know that f(x)=9 when x=0, making the y intercept 9.
So f(0)=a(0-3)(0+5)/(0-16)=9, 15a/16=9, a=48/5=9.6.
Therefore, f(x)=9.6(x-3)(x+5)/(x²-16).
The curve is shown in green and the asymptotes in red.