Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible:

Vertical asymptotes x = -4, x = 5;

x-intercept (-2, 0)

f(x) = something over [(x+4)(x-5) ]

that something wants to be zero when x = -2
so (x+2) on the top
so
(x+2) /[(x+4)(x-5)]

Is that the final answer? Thanks for your help!

To find a rational function that satisfies the given conditions, we can start by considering the vertical asymptotes.

First, let's look at the vertical asymptote at x = -4. This means that the function will become infinitely large (approach positive or negative infinity) as x approaches -4. To express this in the rational function, we can include a factor of (x + 4) in the denominator.

Similarly, for the vertical asymptote at x = 5, we can include a factor of (x - 5) in the denominator of the rational function.

Now let's consider the x-intercept (-2, 0). An x-intercept occurs when the function crosses the x-axis, which means that the y-value is 0. So we know that when x = -2, the function evaluates to 0.

To express this in the rational function, we can include a factor of (x + 2) in the numerator. This way, when x = -2, the numerator will be 0, resulting in a y-value of 0.

Putting it all together, a rational function that satisfies the given conditions could be:

f(x) = (x + 2) / ((x + 4)(x - 5))

Note that there may be other rational functions that also satisfy the given conditions, but this is one example that satisfies the conditions of having vertical asymptotes at x = -4 and x = 5 and an x-intercept at (-2, 0).