A fixed point of a function f is a number c in its domain such that f (c) = c. (The function doesn't move c; it stays fixed.) (a) Sketch the graph of a specific continuous function with domain [0, 1] whose range also lies in [0, 1]. Locate a fixed point of f . (b) Try to draw the graph of a continuous function with domain [0, 1] and range in [0, 1] that does not have a fixed point. What is the obstacle? (c) Use the Intermediate Value Theorem to prove that any continuous function with domain [0, 1] and range in [0, 1] must have a fixed point.

Mathematical reasoning was clear and flow of work was presented clearly.(5 points) Visuals and clear mathematical notation was used to help aid in the arguments. (5 points) Citations were presented as well as a conclusion (summarize your work) and reflection (ex- plain what you learned)