Question

Medals!!!!
The table below shows the outputs y for different inputs x:
Input
(x) 1 1 3 3
Output
(y) 4 2 12 6
Part A: Does the table represent y as a function of x? Justify your answer.
Part B: The total cost f(x), in dollars, for renting a paddleboat for x hours is shown below:
f(x) = 20 + 10x
What is the value of f(120), and what does f(120) represent?

Answer 1

For something to be a function, an x value (input) must not be repeated. We cannot input 1 and get both 4 and 2 as outputs.
Dont forget however, we /CAN/ have same outputs for different inputs, e.g
Input = {1,2,3,4} Output = {0,0,0,0} IS VALID - We got same outputs for unique inputs.
Input = {1,2,3,3} Output = {12,2,32,13} IS INVALID - We repeated inputs and got different outputs.


Part B:
f(x) = 20 +10x. Where x is the number of hours. f(x) represents the cost.
In essence this function tells you how much it costs to rent a boat out for some number of hours. x is hours. f(x) is cost.
So f(120) = Cost of boating for 120 hours.(lots of boating)
To compute the value of f(120) simply plug in 120 for x in the equation given,
f(120) = 20 + 10(120)
f(120) = 20+1200
f(120) = 1220 dollars.