Question

A relation between the different instances of time taken in cycling \((x)\) and the distance covered \((y)\) by two cyclists is given below.
Cyclist 1:
\(\begin{array}{|l|l|l|l|l|l|}
\hline
\text{Time taken (x in minutes)} &20 &30 &20 &50 &60\\\hline
\text{Distance covered (y in miles)} &3 &5 &4 &6 &8\\\hline
\end{array}\)

Cyclist 2:
\(\begin{array}{|l|l|l|l|l|l|}
\hline
\text{Time taken (x in minutes)} &20 &30 &40 &50 &60\\\hline
\text{Distance covered (y in miles)} &3.5 &5 &6 &7 &8\\\hline
\end{array}\)

The relation for cyclist \(1\) is ______ and the relation for cyclist \(2\) is _____.

Answer 1

Detailed step-by-step solution:
Let’s consider all the inputs of each relationship given above.
We know:
1.If all the inputs are not engaged in a relation from \(x\) to \(y,\) then the relation does not qualify as a function.
2. Every input should be related to exactly one output. If that’s not the case, then the relation will not qualify as a function.

Cyclist 1:
Here, \(20\) minutes were taken to cover \(3\) miles and \(4\) miles in separate intervals, i.e., for \(20\) as input, there are two outputs, \(3\) and \(4.\)
It indicates that for a single input, there exists more than one output.
So this relation cannot be considered as a function.

Cyclist 2:
Here, the input-output combinations are: \((20, 3.5), (30, 5), (40, 6), (50, 7), (60, 8)\)
That is, for each value in the input, there exists a unique output.
So this relation will be considered as a function.

So, option D is the correct answer.