1. For the points (-1, 1) and (2, 5), find the distance d between the points and the midpoint M of the line segment which connects them.
2. Determine whether or not each of the following relations represents y as a function of x. Find the domain and range of those relations which are functions.
a. (-1, 1) (0, 5) (1, 7) (-1, 6)
b. y =
3. Find an expression for a function that takes a real number f(x) and performs the following three steps in the order given:
(1) multiply by 2 (2) subtract 4 (3) take the square root
4. Use the function f(x) = 3 – x 2 to find
a. f(-2) b. f( ) c. f(a + 2)
5. Find the domain of f(x) =
6. Use the pair of functions f(x) = and g(x) = to find (-1)
7. Find and simplify the difference quotient for the function f(x) = x2 + 3.
8. The cost, in dollars, to produce x widgets is C(x) = 3x + 32 , x > 0. The price-demand function, in dollars per widget, is p(x) = 30 - x.
a. Find and interpret R(10), where R(x) is the revenue function.
b. Find and interpret P(10), where P(x) is the profit function.
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