1. **State the problem:** We need to find the values of various limits and function values for the piecewise function $g(t)$ at specific points $t=0, 2,$ and $4$ from the graph provided.\n\n2. **Analyze limits and values at $t=0$: **\n- (a) $\lim_{t\to 0^-} g(t)$: approaching 0 from the left, the graph approaches $1$.\n- (b) $\lim_{t\to 0^+} g(t)$: approaching 0 from the right, the graph approaches a value different than from the left (around $3$), so $\lim_{t\to 0^+} g(t) = 3$.\n- (c) $\lim_{t\to 0} g(t)$: since left and right limits differ, this limit **does not exist** (DNE).\n\n3. **Analyze limits and values at $t=2$: **\n- (d) $\lim_{t\to 2^-} g(t) = 4$ (the limit from the left is about 4).\n- (e) $\lim_{t\to 2^+} g(t) = 1$ (the limit from the right is about 1).\n- (f) $\lim_{t\to 2} g(t)$: since left and right limits differ, this limit **does not exist** (DNE).\n- (g) $g(2) = 2$ (value of the function at $t=2$ is given as 2, distinct from the limits).\n\n4. **Analyze limit at $t=4$: **\n- (h) $\lim_{t\to 4} g(t) = 5$ (the graph approaches about 5 as $t$ approaches 4).\n\n**Summary:**\n- (a) $\lim_{t\to 0^-} g(t) = 1$\n- (b) $\lim_{t\to 0^+} g(t) = 3$\n- (c) $\lim_{t\to 0} g(t)$ does not exist because left and right limits differ.\n- (d) $\lim_{t\to 2^-} g(t) = 4$\n- (e) $\lim_{t\to 2^+} g(t) = 1$\n- (f) $\lim_{t\to 2} g(t)$ does not exist because left and right limits differ.\n- (g) $g(2) = 2$\n- (h) $\lim_{t\to 4} g(t) = 5$