Please review and answer the questions below..
Question 1. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 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.
Question 2. 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
Question 3. Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f(x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi part relations so consider all parts when determining if they are functions.
a. f(x) = x + 4
b. f(x) = 3 if x>2 otherwise f(x) = -2
c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0
Question 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 thoroughly.
a. The time it takes you to get to work as a function the speed at which you drive
b. The probability of getting into a car accident as a function of the speed at which you drive
c. A person's height as a function of the person's age (from age 0 to 100)