Let's analyze the graph and answer the given limit and function value questions.

Step 1: Understanding the Graph

• The function has a closed dot at $(1,1)$, meaning $f(1) = 1$.
• The function has an open dot at $(1,2)$, meaning the function is not defined at $y = 2$ for $x = 1$, but it approaches this value from the left or right.
• The function behaves piecewise, changing its path at different intervals.

Answering the Questions

50. $\lim_{x \to 1^-} f(x)$ (Left-hand limit at $x = 1$)

• As $x$ approaches 1 from the left,