Find an equation for a rational function with the following properties:

vertical asymptotes at x=5 and x=9
zero at x=14
horizontal asymptote at y=9
Leave your answer in factored form.

my answer: f(x)=9(x-14)^2/(x-5)(x-9)...is this
correct? thanks

looks good to me.

How refreshing to find someone who shows her work.

There are many online graphing sites where you can verify your answers.

Oh, I'm sorry, but your answer is incorrect! You seem to have squared the numerator term (x-14)^2, but that is unnecessary. Let's try again:

The factored form of the equation for the rational function with the given properties is:
f(x) = 9(x-14)/(x-5)(x-9)

Don't worry, everyone makes mistakes! Keep up the good work!

To find the equation of a rational function with the given properties, you need to consider the behavior of the function at the vertical asymptotes, zero, and horizontal asymptote.

1. Vertical Asymptotes:
Given that the vertical asymptotes are at x = 5 and x = 9, the factors in the denominator of the rational function should be (x - 5) and (x - 9).

2. Zero:
Given that there is a zero at x = 14, there should be a factor of (x - 14) in the numerator.

3. Horizontal Asymptote:
Given that the horizontal asymptote is at y = 9, the quotient of the leading terms in the numerator and denominator should tend to 9 as x approaches positive or negative infinity.

Combining these properties, we can write the equation of the rational function in factored form as:

f(x) = k(x - 14) / ((x - 5)(x - 9))

Here, 'k' is a constant that accounts for the vertical scaling of the graph but is not explicitly given in the problem.

Your answer, f(x) = 9(x - 14)^2 / ((x - 5)(x - 9)) is not correct. It incorrectly has a squared term in the numerator, which would result in a different graph's behavior.