Question

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. (5 points)

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? (5 points

Answer 1

Part A)
The table doesn't represent y as a function of x.
Why? One reason is that 1 or 3 is the first element in more than one ordered pair.
Part B)
f(x) = 10x + 20
f(120)= 10*120 + 20 = 1200 + 20 = 1220
f(120) represents cost of boating for 120 hours.

Answer 2

Answer with explanation:

Part A:

• A relation is said to be a function where each input has only a single output.

We usually take the input variable as 'x' and the output variable as 'y'.

In the given table, we can see that 1 is the input value corresponding to 4 and 2 both.

i.e. one input value corresponds to two different output values that contradicts the definition of the function.

Thus the given table doesn't represent any function.

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

`f(x) = 20 + 10x`

At x= 120 ,
`f(120) = 20 + 10(120)=20+1200=1220`

It represents that the total cost for renting a paddle-boat for 120 hours is $1220.