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MAT 117 Unit C Problem Set Directions: Show all work 1. Consider the function f (x) = 3x' + 4x - 2. a. [1 pt] Find f(3). b. [1 pts] Find f(a), an expression of a. c. [2 pts] Find f(x + h), an expression of x and h. d. [2 pts] Find f (x + h) - f (x), an expression of x and h. Simplify your answer.e. [2 pts] Suppose h # 0. Find 4*+p)-/0), an expression of x and h. Simplify your answer. A 2. A cellphone company offers the following plan: $20 per month buys 60 minutes. Additional time costs $0.40 per minute. a. [3 pts] Represent this plan mathematically by writing the total monthly cost, C, as a piecewise function of the number of calling minutes, r. 20 + 0.4(t-60) 20 - 0.4t - 24 0.4t - 4b. [3 pts] Find and interpret the quantities C(30) and C(100) C(30) = 20, C(100) = 36 c. [3 pts] Graph v = C(t) fort values between 0 and 200 minutes. Indicate your scale on both the horizontal and vertical axes, and be sure to label what quantities each axis represents 3. A ball is thrown from an initial height of 7 feet with an initial upward velocity of 48 ft's. The ball's height h (in feet) after { seconds is given by h =7+48t - 16t-a. [4 pts] Algebraically find all values of r for which the ball's height is 39 feet. b. [4 pts] Algebraically find the maximum height of the ball