Download Math 121 Test 2: Midpoint, Distance, Circles, Quadratics, Lines, Inequalities, Functions and more Exams Algebra in PDF only on Docsity!
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.
- (a) Find the midpoint of (3, −2) and (7, −4).
(b) Find the distance between (3, −2) and (7, −4).
- A circle is centered at (− 1 , 2) and passes through the point (2, −6). Find the radius of the circle, and then write the equation of the circle.
- (a) Find f (1), f (5) and f (7) for the piecewise defined function f (x) =
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.
- Find the equation of the line through the points (4, 5) and (7, −1). Write your answer in slope-intercept form.
- Let f (x) = ax^2 + bx + c be a quadratic where a 6 = 0.
(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?
- Use the graph of g to sketch (a) y = g(x + 3) and (b) y = g(x + 3) − 2 and (c) y = g(−x).
Name:
- A manufacturer produces a product at a cost of $22.80 per unit. The manufacturer has a fixed cost of $400.00 per day. Each unit retails for $37.00. Let x be the number of units produced in a day.
(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).
- The number of board-feet of lumber that can be obtained from a log 16 feet long is linearly related to diameter as follows. If the diameter is 16 inches, then 90 board-feet are obtained; if the diameter is 22 inches, then 180 board-feet are obtained.
(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 farmer has 1200 feet of fencing to build a rectangular pen that is subdivided into two separate rectangular regions for his pigs and dogs (see sketch below).
(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.
