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Plotting a piecewise defined function

mark

Define f(x) by

f(x) = \begin{cases} x^2 & \text{if } \: x < 2 \\ c - x & \text{if } \: x\geq2 \end{cases}.
  1. Sketch the graph of f for c=1.
  2. State precisely why f is discontinuous at x=1 when c=1.
  3. For what value of c is f continuous for all real numbers?
  4. Sketch the graph of f when for your choice of c from part 3.

Note: I think this problem should be very doable by hand. It might be fun to produce a Desmos plot to answer the question, though.

mearing

  1. The graph is discontinuous because the limit from the left and right do not converge on the same number.

  2. When c=6 the graph is continuous for all real numbers.