let $g$ be a continuous function on the closed interval $-2,4$. a few values of $g$ are given in this…

let $g$ be a continuous function on the closed interval $-2,4$. a few values of $g$ are given in this table:\n$x$ -2 0 2 4\n$g(x)$ 1 -2 3 -5\nwhich intervals must contain a solution to $g(x)=-1$?\nchoose all answers that apply:\na $-2,0$\nb $0,2$

let $g$ be a continuous function on the closed interval $-2,4$. a few values of $g$ are given in this table:\n$x$ -2 0 2 4\n$g(x)$ 1 -2 3 -5\nwhich intervals must contain a solution to $g(x)=-1$?\nchoose all answers that apply:\na $-2,0$\nb $0,2$

Answer

Explanation:

Step1: Recall Intermediate - Value Theorem

The Intermediate - Value Theorem states that if (y = g(x)) is continuous on the closed interval ([a,b]), and (k) is a number between (g(a)) and (g(b)), then there exists at least one number (c) in the interval ((a,b)) such that (g(c)=k).

Step2: Check interval ([-2,0])

We have (g(-2) = 1) and (g(0)=-2). The value (k = - 1) is between (g(-2)=1) and (g(0)=-2). Since (g(x)) is continuous on ([-2,0]), by the Intermediate - Value Theorem, there must be a (c\in(-2,0)) such that (g(c)=-1).

Step3: Check interval ([0,2])

We have (g(0)=-2) and (g(2)=3). The value (k=-1) is between (g(0)=-2) and (g(2)=3). Since (g(x)) is continuous on ([0,2]), by the Intermediate - Value Theorem, there must be a (c\in(0,2)) such that (g(c)=-1).

Answer:

A. ([-2,0]) B. ([0,2])