Find a possible equation for the function with a graph having the given features.
$x$-intercepts, $(-2,0)$ and $(4,0), y$-intercept, $(0,-8)$, vertical asymptote, $x=1$, horizontal asymptote, $y=1$
Choose the possible equation for the function.
$f(x)=\frac{(x-4)(x+2)}{(x-1)^{2}}$
$f(x)=\frac{(x-4)}{(x-1)^{2}}$
$f(x)=\frac{(x-1)^{2}}{(x-4)(x+2)}$
$f(x)=\frac{(x-4)(x+2)}{(x-1)}$

Step 1 ：The function is a rational function because it has vertical and horizontal asymptotes. The x-intercepts are the roots of the numerator and the vertical asymptote is the root of the denominator. The y-intercept is the value of the function at x=0. The horizontal asymptote is the limit of the function as x approaches infinity or negative infinity.

Step 2 ：Consider the following possible equations for the function: \(f(x)=\frac{(x-4)(x+2)}{(x-1)^{2}}\), \(f(x)=\frac{(x-4)}{(x-1)^{2}}\), \(f(x)=\frac{(x-1)^{2}}{(x-4)(x+2)}\), \(f(x)=\frac{(x-4)(x+2)}{(x-1)}\).

Step 3 ：By analyzing the results, we can see that the first function \(f(x)=\frac{(x-4)(x+2)}{(x-1)^{2}}\) has the correct x-intercepts (0,0), y-intercept (-8), vertical asymptote (-oo), and horizontal asymptote (1,1).

Step 4 ：\(\boxed{f(x)=\frac{(x-4)(x+2)}{(x-1)^{2}}}\) is the correct equation for the function with the given features.