Final answer:
To determine an equation of a rational function with a vertical asymptote at x=2 and a removable discontinuity at x=-3, consider the characteristics of these features and create an equation that satisfies them.
Step-by-step explanation:
To determine an equation of a rational function with a vertical asymptote at x=2 and a removable discontinuity at x=-3, we can start by considering the characteristics of these features. A vertical asymptote at x=2 means that the function approaches infinity or negative infinity as x approaches 2. A removable discontinuity at x=-3 means that the function has a hole at x=-3, where it is undefined but can be filled in.
One possible equation that satisfies these characteristics is:
f(x) = (x+3)(x-2)/(x-2)
In this equation, we have (x+3) in the numerator to ensure a removable discontinuity at x=-3, and (x-2) in both the numerator and denominator to create a vertical asymptote at x=2.