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6 Nov 2019
Let f(x) = Find a and b so that the graph of f(x) does not have any jumps. A fixed point of a function f is a number c in its domain such that f(c) = c. Sketch the graph of a continuous function with domain[0, 1] whose range also lies in [0, 1]. Locate a fixed point of f. 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. Why is it not possible; what is the obstacle? Use the Intermediate Value Theorem and a picture to prove that any continuous function with domain[0, 1] and range a subset of [0, 1] must have a fixed point. (Hint: what line must a fixed point lie on?) Show transcribed image text
Let f(x) = Find a and b so that the graph of f(x) does not have any jumps. A fixed point of a function f is a number c in its domain such that f(c) = c. Sketch the graph of a continuous function with domain[0, 1] whose range also lies in [0, 1]. Locate a fixed point of f. 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. Why is it not possible; what is the obstacle? Use the Intermediate Value Theorem and a picture to prove that any continuous function with domain[0, 1] and range a subset of [0, 1] must have a fixed point. (Hint: what line must a fixed point lie on?)
Show transcribed image text Lelia LubowitzLv2
6 Nov 2019