1. **State the problem:** We are asked to find various limits and function values of $g(t)$ at points $t=0$, $t=2$, and $t=4$ based on the graph description. 2. **Recall limit definitions:** - The left-hand limit $\lim_{t \to a^-} g(t)$ is the value $g(t)$ approaches as $t$ approaches $a$ from the left. - The right-hand limit $\lim_{t \to a^+} g(t)$ is the value $g(t)$ approaches as $t$ approaches $a$ from the right. - The limit $\lim_{t \to a} g(t)$ exists if and only if the left and right limits are equal. 3. **Analyze each part:** (a) $\lim_{t \to 0^-} g(t)$: From the left of 0, the graph is near $y = -2$. (b) $\lim_{t \to 0^+} g(t)$: From the right of 0, the graph is slightly above $-2$ (open circle), so the limit is slightly above $-2$. (c) $\lim_{t \to 0} g(t)$: Since left and right limits differ (left is $-2$, right is slightly above $-2$), the limit does not exist. (d) $\lim_{t \to 2^-} g(t)$: Approaching 2 from the left, the graph approaches the filled dot at $(2,2)$, so limit is 2. (e) $\lim_{t \to 2^+} g(t)$: Approaching 2 from the right, the graph approaches the open circle at $(2,4)$, so limit is 4. (f) $\lim_{t \to 2} g(t)$: Left and right limits differ (2 and 4), so limit does not exist. (g) $g(2)$: The filled dot at $(2,2)$ means $g(2) = 2$. (h) $\lim_{t \to 4} g(t)$: The graph continues upward past $t=4$ smoothly, so the limit is the $y$-value at $t=4$, which is about 4. **Final answers:** (a) $-2$ (b) slightly above $-2$ (c) does not exist (d) $2$ (e) $4$ (f) does not exist (g) $2$ (h) $4$