\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the function \(f\) defined on \(\mathbb{R}\) by:$$ f(x) = \begin{cases} -x & \text{if } x < 1 \\ x^2 - 2 & \text{if } x \ge 1 \end{cases} $$The graph of \(f\) is shown below:
  1. Graphically, conjecture whether the function \(f\) is continuous at \(x=1\).
  2. Prove your conjecture using the mathematical definition of continuity.

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.