1. Determine whether each of the following is a function or not.
(a) f(x) = 1 if x>1
= 0 otherwise
(b) f(x) = 2 if x>0
= -2 if x<0
= 2 or -2 if x = 0
= 0 otherwise
(c) f(x) = 5/x
2. Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 60 cups. But when you raise your price to $2 you only sell 30 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.
3. Take a look at the table below and write out an equation for f(x)
x -2 -1 0 1 2
f(x) -1 1 3 5 7
4. For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning.
a. How fast it takes you to get to work as a function of how fast you drive.
b. Probability of getting into a car accident as a function of how fast you drive.
c. Your height as a function of age (from age 0 to 100)