MATH 115 Quiz 1 Summer 2022
1) Graph the equation given: y = -1/3 x + 8
2) Use the graph to determine the function’s domain and range. Determine the intervals on which the function is increasing, decreasing, and constant.
Given functions f and g, perform the indicated operations.
3) f(x) = -3x + 9, g(x) = 5x – 4 Find f + g.
4) f(x) = 5 + 11x, g(x) = 3x + 25 Find f – g.
5) f(x) = x – 12, g(x) = -2x – 17 Find f/g.
6) The function f(t) = -0.15t2 + 0.53t + 30.4 models the U.S. population in millions, ages 65 and older, where t represents years after 1990. The function g(t) = 0.56t2 + 12.6t + 105.6 models the total yearly cost of Medicare in billions of dollars, where t represents years after 1990. Find (g/f)(9).
7) A firm is considering a new product. The accounting department estimates that the total cost, C(x), of producing x units will be C(x) = 60x + 7870. The sales department estimates that the revenue, R(x), from selling x units will be R(x) = 70x, but that no more than 955 units can be sold at that price. Find and interpret (R – C)(753).
8) Find the distance and midpoint between the pair of points ( -2, 9) and ( 13, -5)
9) Two apartment tenants have a total of 600 feet of fencing to enclose a rectangular garden and subdivide into two smaller gardens, one for each of them, by placing the fencing parallel to one of the sides. Express the area of the entire garden, A, as a function of x. (bonus)