$y=x(x+4)(x-3)$ as shown in the graph.
Work Step by Step
Step 1. Identify the zeros as $x=-4,0,3$; thus the equation contains factors $x^k(x+4)^m(x-3)^n$ where $k,m,n$ are positive integers. Step 2. Identify the end behaviors as $x\to-\infty,y\to-\infty$ and $x\to\infty,y\to\infty$ based on the given conditions. Step 3. We can identify the leading coefficient to be positive and the degree to be odd with a minimum of $k=m=n=1$ Step 4. We can write an example function as $y=x(x+4)(x-3)$ as shown in the graph.