which interval for the graphed function has a local minimum of 0?\n-3, -2\n-2, 0\n1, 2\n2, 4

Answer

A local minimum is a point where the function value is less than or equal to the values of the function in a small interval around it.

For the interval $[-3,-2]$, the function value at $x = - 2.5$ is $0$. And in the small - interval around this part of $[-3,-2]$, the function value is $0$ at $x=-2.5$.
For the interval $[-2,0]$, the function value at $x = 0$ is $0$, but the function dips below $0$ in the interval $[-2,0]$ (e.g., at $x=-1.56$ where $y = - 6$).
For the interval $[1,2]$, the function values are all above $0$.
For the interval $[2,4]$, the function values are all above $0$.

$[-3,-2]$