1. The problem asks to find the limits and function values for the function $f$ at specific points based on the graph description. 2. Recall the definitions: - The left-hand limit $\lim_{x \to a^-} f(x)$ is the value $f(x)$ approaches as $x$ approaches $a$ from the left. - The right-hand limit $\lim_{x \to a^+} f(x)$ is the value $f(x)$ approaches as $x$ approaches $a$ from the right. - The limit $\lim_{x \to a} f(x)$ exists if and only if the left-hand and right-hand limits are equal. - The function value $f(a)$ is the value of the function at $x=a$. 3. From the graph description for $f$: - At $x=2$, there is an open circle at $(2,1)$ and the curve jumps to about $y=3$. - At $x=4$, the curve peaks at $(4,4)$. 4. Evaluate each quantity: (a) $\lim_{x \to 2^-} f(x)$: Approaching 2 from the left, the curve approaches the open circle at $y=1$, so the limit is $1$. (b) $\lim_{x \to 2^+} f(x)$: Approaching 2 from the right, the curve jumps to about $y=3$, so the limit is $3$. (c) $\lim_{x \to 2} f(x)$: Since left and right limits differ ($1 \neq 3$), the limit does not exist. (d) $f(2)$: The function value at $2$ is the open circle at $y=1$, so $f(2) = 1$. (e) $\lim_{x \to 4} f(x)$: The curve peaks at $(4,4)$ smoothly, so the limit is $4$. (f) $f(4)$: The function value at $4$ is the peak point, so $f(4) = 4$. Final answers: (a) $1$ (b) $3$ (c) Does not exist (d) $1$ (e) $4$ (f) $4$