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

Explanation:

Step1: Understand local - minimum concept

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 in the table

We have the following function values: $f(-2)=-8$, $f(-1)=-3$, $f(0)= - 2$, $f(1)=4$, $f(2)=1$, $f(3)=3$.

Step3: Compare the values

We see that $f(-2)=-8$ is the smallest value among the given points. The ordered - pair corresponding to $x = - 2$ is $(-2,-8)$. But among the given options, we need to find the closest to a local minimum. The value of the function is decreasing from $x=-2$ to $x = - 1$ and then increasing from $x=-1$ to $x = 0$. So, the point $(-1,-3)$ is a local minimum candidate. Among the options, the point closest to a local minimum is $(-1,-3)$.

Answer:

$(-1,-3)$