1. The problem asks if the Intermediate Value Theorem (IVT) can be used to conclude that the equation $g(x) = -\frac{3}{4}$ has a solution for $x$ in the interval $[100, 101]$. 2. The Intermediate Value Theorem states that if a function $g$ is continuous on a closed interval $[a, b]$ and $N$ is any number between $g(a)$ and $g(b)$, then there exists at least one $c$ in $[a, b]$ such that $g(c) = N$. 3. From the table, $g(100) = -1$ and $g(101) = -\frac{1}{2} = -0.5$. 4. We want to check if $-\frac{3}{4} = -0.75$ lies between $g(100)$ and $g(101)$. 5. Since $-1 < -0.75 < -0.5$, $-\frac{3}{4}$ is indeed between $g(100)$ and $g(101)$. 6. However, to apply the IVT, $g$ must be continuous on $[100, 101]$. The problem does not provide information about the continuity of $g$. 7. Therefore, without knowing if $g$ is continuous, we cannot use the IVT to guarantee a solution to $g(x) = -\frac{3}{4}$ on $[100, 101]$. Final answer: No, because we do not know if $g$ is continuous on the interval $[100, 101]$, so the Intermediate Value Theorem cannot be applied.