Question

Find a rational function with x-intercepts –2 and 5, y-intercept 5, and vertical asymptotes x = 3 and x = 6. State the horizontal asymptote of the graph of the function.

Answer 1

An x intercept at x = -2 and 5 means the numerator has a zero at x = -2 and x=5

The rational function f that has a vertical asymptote at x = 3 and x=6, then the denominator of the rational function contains the term (x - 3) and (x-6).

So the rational function with x-intercepts –2 and 5, y-intercept 5, and vertical asymptotes x = 3 and x = 6

.

The horizontal asymptote of the graph of the function

is since both polynomials are the same degree, divide the coefficients of the highest degree terms

i.e The horizontal asymptote is at .