what ordered pair is closest to a local minimum of the function, f(x)?\n(-1, -3)\n(0, -2)\n(1, 4)\n(2…

Explanation:

Step1: Understand local minimum

A local minimum is a point where the function value is less than or equal to the values at nearby points.

Step2: Analyze the function values

We have the following function - value pairs: $(-2,-8),(-1, - 3),(0,-2),(1,4),(2,1),(3,3)$.

Step3: Compare the values

We see that $f(-2)=-8$ is the smallest value among the given points. But we need to check if it is a local - minimum. Since we don't have values for $x$ less than $-2$, we look at the trend. The value of the function increases from $x=-2$ to $x = - 1$ (from $-8$ to $-3$), then to $x = 0$ (to $-2$), then to $x = 1$ (to $4$), then decreases to $x = 2$ (to $1$) and then increases to $x = 3$ (to $3$). The point $(-2,-8)$ is a local minimum. But among the given options, we need to find the closest one. The closest point to $(-2,-8)$ among the options is $(-1,-3)$.

Answer:

$(-1,-3)$