1. Stating the problem: We are asked to find two limits based on the description of the graph of a function $f(x)$. 2. For part (a), find $\lim_{x \to 0} f(x)$. - The graph passes through the origin (0,0). - Since the function is continuous, the limit at $x=0$ is simply the function value at 0. - Thus, $\lim_{x \to 0} f(x) = 0$. 3. For part (b), find $\lim_{x \to 2} f(x)$. - The graph shows a solid dot at approximately $(2,-3)$. - This indicates the function value at 2 is $f(2) = -3$. - However, there is also an open circle near $(2,1)$, indicating a hole/discontinuity at that point. - The limit $\lim_{x \to 2} f(x)$ depends on where the function values approach as $x$ approaches 2. - Since the graph decreases through $(2,-3)$ with a solid dot and there's a hole at $(2,1)$, the limit equals the value of the function approaching 2. - Since the open circle suggests the value at 1 is not included, but the function approaches $-3$, the limit is $-3$. 4. Final answers: - $\boxed{\lim_{x \to 0} f(x) = 0}$ - $\boxed{\lim_{x \to 2} f(x) = -3}$ These values match the continuity and the provided points on the graph.