1. **State the problem:** We need to draw a function $f$ with the following properties: - $f(0)=-2$, $f(-3)=4$, $f(5)=1$ - $f(x)$ decreases on $x<0$ and $x>5$ - $f(x)$ increases on $x<-3$ and $05$. - As $x \to \infty$, $f(x) \to -4$ (horizontal asymptote). - As $x \to -\infty$, $f(x) \to -\infty$. 3. **Construct a piecewise description:** - From $-\infty$ to $-3$, $f$ increases from $-\infty$ to 4. - From $-3$ to $0$, $f$ decreases from 4 to $-2$. - From $0$ to $5$, $f$ increases from $-2$ to 1. - From $5$ to $\infty$, $f$ decreases from 1 to $-4$. 4. **Summary:** The function has a local maximum at $x=-3$ with value 4, a local minimum at $x=0$ with value $-2$, and another local maximum at $x=5$ with value 1, then approaches $-4$ as $x \to \infty$. 5. **Desmos function:** A possible function matching these conditions is complicated but can be approximated by a smooth curve passing through the points and following the increasing/decreasing intervals and limits. "slug": "function behavior","subject": "calculus","desmos": {"latex": "f(x)","features": {"intercepts": true,"extrema": true}},"q_count": 1