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Question 36785: Please explain functions, relations and arguments. I need guidance to answer the following questions:
1. Which of the following are functions? Explain reasoning for a, b, and c.
a. f(x) = 2 if x>1
f(x) = -1 otherwise
b. f(x) = 5 if x>0
f(x) = -5 if x<0
c. f(x) = 10/x
2. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonad 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.
3. Take a look at the table below and write out an equation for f(x).
x -2 -1 0 1 2
f(x) -5 -2 1 4 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 thoroughly.
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 your drive.
c. Your height as a function of age (from age 0 to 100).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Which of the following are functions? Explain reasoning for a, b, and c.
a. f(x) = 2 if x>1
f(x) = -1 otherwise
b. f(x) = 5 if x>0
f(x) = -5 if x<0
c. f(x) = 10/x
They are all functions, because " for each value of "x" there is
only one value of "y".
Realations allow an x value to have several y value associates.
2. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonad 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.
You have two points to work with : (Price, # of cups)
(2,120) and (3,60)
The linear form is cups = (slope)(price)+ b
slope = (120-60)/(2-3)=-60
Then 120=-60(2)+b
b=240
Your equation is C=-60p+240
3. Take a look at the table below and write out an equation for f(x).
x -2 -1 0 1 2
f(x) -5 -2 1 4 7
Since there is a common difference of +3 in the y-values
the relation is linear, i.e. y=mx+b
Use two of the points to get the equation, as follows:
Points: (0,1) (2,7)
slope = (7-1)/2= 3
1=3(0)+b
b=1
y=3x+1
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. How fast it takes you to get to work as a function of how fast you drive.
Linear: as average speed increases, time decreases
b. Probability of getting into a car accident as a function of how fast your drive.
Linear: as speed increases, probability of having an accident increases.
c. Your height as a function of age (from age 0 to 100).
non-linear: age increases in a constant way; height does not.
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