Write an equation for a rational function with: Vertical asymptotes at $x=4$ and $x=2$ $x$ intercepts at $x=-5$ and $x=-6$ Horizontal asymptote at $y=7$ \[ y= \] Quest:ํำ Help: $\square$ Message instructor > Next Question

Step 1 ：Vertical asymptotes occur when the denominator of a rational function is equal to zero. So, we need to include factors of \((x-4)\) and \((x-2)\) in the denominator.

Step 2 ：The x-intercepts of a function occur when the function is equal to zero. So, we need to include factors of \((x+5)\) and \((x+6)\) in the numerator.

Step 3 ：A horizontal asymptote at \(y=7\) means that the degree of the numerator and denominator must be the same and the ratio of the leading coefficients must be 7.

Step 4 ：Let's write the function in the form \(y=\frac{A(x+5)(x+6)}{(x-4)(x-2)}\) and find the value of A such that the ratio of the leading coefficients is 7.

Step 5 ：The leading coefficient of the numerator is A and the leading coefficient of the denominator is 1. So, A must be equal to 7 to make the ratio of the leading coefficients equal to 7.

Step 6 ：Substituting A=7 into the equation, we get the final equation for the rational function: \(\boxed{y=\frac{7(x+5)(x+6)}{(x-4)(x-2)}}\)