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The instructions and problems for math 121 test 2, held on february 7, 2006. The test covers various topics in mathematics, including finding midpoints and distances, dealing with circles, quadratic functions, lines, inequalities, absolute values, functions of functions, difference quotient, cost-revenue-profit analysis, and linear functions. Students are required to solve each problem and show their work.
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Math 121, Test 2, February 7, 2006
Name:
Instructions. Do each of the following 12 problems. Each problem is worth 5pts. Show all appropriate details in your solutions. No calculators are not allowed on the first 9 problems.
(b) Find the distance between (3, −2) and (7, −4).
x^3 + 1 −x ,^ if^ x <^ 1; 0 if 1 ≤ x ≤ 5; x − 2 if x > 5.
(b) Find the domain of f (x) =
7 − x and state your answer in interval form.
(a) If a > 0, does the function f have a minimum or a maximum?
(b) What is the formula for finding the vertex of f?
(c) What is the range of the function h(x) = −4(x + 2)^2 − 3?
Name:
(a) Write the cost C as a function of x.
(b) Write the revenue R as a function of x.
(c) Write the profit P as a function of x (remember: profit = revenue - cost).
(a) Use this data to find the formula of a linear function f (x) which gives the number of board-feet of a 16 foot log when x is the diameter in inches of the log.
(b) Use f to determine how many board-feet a log 16 feet long and 2 feet in diameter would produce?
(a) Write the length l as a function of the width w.
(b) Write the total area A as a function of w.
(c) Find the dimensions that produce the greatest enclosed area.