Problem 1 - For the polynomial f (x) = 0.025x⁵ - 0.0625x⁴ - 0.333x³ + x² - 2

(a) Calculate the value of the function for x = -1, - 0.5, 0, 0.5, 1, 1.5, 2, 2.5

(b) Plot the polynomial for - 4 ≤ x ≤ 4

(c) Find f(9)

(d) Find the value(s) of x for which f(x) = 0

Problem 2-The following data points are taken from a process believed to follow a power function.

(a) Find a quadratic (e.g, x² +...) polynomial that fits the data.

(b) Plot the data points against the function in "a" above.

Problem 3- (a) On a single figure window, plot the function ?? = 10???? for m = -2, -1, 0, 1, 2 (use rectilinear axes unless specified otherwise).

(b) For what values of m does the function pass through the origin?

(c) On a single figure window, plot the function ?? = ??^?? for m = -0.5, -0, 0.5, 1, 2 (use rectilinear axes unless specified otherwise).

(d) For what values of m does the function pass through the origin?