Question

1. draw a function that has a local maximum at (-3,2) and a local minimum at (2,-1).

Explanation:

Step1: Mark key points

Mark the points $(-3,2)$ and $(2, - 1)$ on the coordinate - grid.

Step2: Sketch increasing and decreasing parts

Draw a curve that is increasing to the left of $x=-3$, then decreasing from $x = - 3$ to $x = 2$, and then increasing again to the right of $x = 2$. For example, a cubic - like function can be drawn. Start from the bottom - left, go up to the local maximum at $(-3,2)$, then go down to the local minimum at $(2,-1)$, and then go up again towards the top - right.

Answer:

A hand - drawn curve on the given grid with a local maximum at $(-3,2)$ and a local minimum at $(2,-1)$ following the described increasing and decreasing behavior.