Question

The table below shows the squares of different numbers:

Number
(x) 2 −2 3 −3
Square of the number
(y) 4 4 9 9


Part A: Does the table represent y as a function of x? Justify your answer. (5 points)

Part B: The total cost f(x), in dollars, for renting a rowboat for x hours is shown below:

f(x) = 20 + 3x

What is the value of f(150), and what does f(150) represent? (5 points)

Answer 1

Part A:

Yes this is a function of x. Specifically the function is f(x) = x^2
The inputs (x) are squared to get the outputs (y).
For example,
f(x) = x^2
f(-3) = (-3)^2 <<--- input is x = -3
f(-3) = 9 <<--- output is 9
The pair of values -3 and 9 are shown in the table (column on the very right side)

The fact that each input leads to exactly one output is what makes this a function. If we had an input lead to multiple outputs, then it wouldn't be a function.

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Part B

Replace every x with 150 and then use the order of operations PEMDAS to simplify

f(x) = 20+3x
f(x) = 20+3*x
f(150) = 20+3*150 <<--- x has been replaced with 150
f(150) = 20+300
f(150) = 320
So the value of f(150) is 320
The input is 20
The output is 320
x is the number of hours
y or f(x) is the total cost

So this means f(150) = 320 represents the idea that 150 hours of renting the rowboat leads to a total cost of $320