1. The problem asks to find $$\lim_{x \to 1} f(x)$$ given the graph. 2. We analyze the behavior of the function near $$x=1$$ from both sides. 3. From the left side (values approaching 1 but less than 1), the graph is part of the parabolic shape that dips down to (0,0) and rises toward a height. 4. Observing the graph near $$x=1$$ from the left, the function values approach 2. 5. From the right side (values just greater than 1), the graph is a line rising upward starting just right of (1,1) with an open circle at (1,1). 6. Approaching $$x=1$$ from the right, the values also approach 2. 7. Since both left and right limits as $$x \to 1$$ approach 2, the limit exists and equals 2. 8. Note the function value at $$x=1$$ is not 2 (open circle), but this does not affect the limit. Therefore, $$\lim_{x \to 1} f(x) = 2.$$