Find a rational function that satisfies the given conditions

Question

Vertical asymptotes: x=1, x=-2

X-intercept: (-5,0)

Answer 1

Well, for the vertical asymptotes, the function must have a zero denominator when x=1 or x=-2.

This forces x-1 and x+2 in the denominator.

FOr an x-intercept to be -5, the graph must cross the x-axis at x=-5 which means -5 is a solution.

Therefore, the numerator must be zero when x=-5.

This forces x+5 in the numerator.

The function is:

y = (x+5)/( (x-1)(x+2))