1. The cost function for making a certain product is
C(x) = 3x + 5 per item, where x is the number of items.
The selling price per item is
p(x) = -x/2 + 10
The revenue received if x items are sold is
R(x) = x*p(x)
The profit made if x items are sold is
Profit(x) = R(x) - C(x)
Using the graphing calculator
a. Plot C(x)
b. Plot R(x)
c. Plot Profit(x)
d. What is number of items that should be made and sold if Profit(x) is a maximum?
e. What is the maximum profit?
2. Given the following function: y = x3 - 4x2 - x -1 for -1 <= x <= 4
a. Plot the function.
b. What is the maximum value for y?
c. What is the minimum value for y?
d. What is the range of y?
3. Write the new equation which shifts the following equations.
a. y = 2x + 5, new equation is shifted 3 units to the right
b. y = -4x + 1, new equation is shifted 2 units down
c. (x -4)2 + (y + 2)2 = 32, new equation is shifted 2 units to the left and 1 unit up
d. y = (x - 1)2 + 2, new equation is shifted1 unit to the right and 3 units up
e. y = 2x, new equation is shifted 1 unit to the left and 2 units down
4. What is the domain and range of the following functions? Write answer in interval notation.
a. y = -x2 + 4x - 4
b. y = x4 + 2x3 - 5x2 - 6x
c. y = sqrt(x - 4) - 3
d. y = sqrt(x2 - 4) - 3
e. y = sqrt[ 25 - (x+2)2 ] + 3