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Problem 1 Bisection method (15+ 35 = 50 points) (a) Write a MATLAB .m function named bisection.m that computes a real root for any non- linear equation of the form f(1) = 0 within mumerical tolerance s. where f is contimions in the interval (a, b). Your MATLAB function bisection.m should take the inputs: a. b. f.e and return an approximation for the root dapprix. It is a good practice (but not mandatory) to pass an additional input for maximum mumber of iterations. The function f should be defined in another MATLAB function func.m. (b) For any nonnegative integer n, the function pr() is defined recursively as Port(x) = 2.rp. (r) - Pri(ar). where Por) = 1, P.) = 1. It is known that prex) has n real roots, and all of them are located in the interval (-1,1). Write a MATLAB code Yourlastnameyourfirstname Hw3p1.mn that plots a graph of the func- tion py(1). By visually inspecting this plot, call the function bisection.m from part (a) in your code Yourlastnameyourfirstname Hw3p1.m to mmerically compute all 4 roots of p.() within tolerance e = 10 4. Recall that bisection.m in turn calls appropriately defined func.m