Write an equation of a rational function that satisfies all of these conditions below.

Question

y-intercept of -5

● x-intercepts at x=-1 and x= 5

● Hole at x = -2

● Horizontal asymptote at y = 6

● No vertical asymptotes

Answer 1

hole x=-2 usually means put x+2 in the denominator, but that also creates a vertical asymptote at x=2

zeros -1 and 5, means usually have (x+1)(x-5) in the numerator

y intercept -5

asymptote y=6 usually means have a 6 coefficient in the numerator

no vertical asymptotes seems to conflict with the discontinuity

one way around this is do a piece wise function