Question

A relation between the input $\left(x\right)$ and the output $\left(y\right)$ is given in the table below.

$\begin{array}{cc}\left(x\right)& \left(y\right)\\ -3& 4\\ -2& -1\\ 0& 5\\ 2& 10\\ -1& 8\\ 3& 0\\ -3& -2\\ -2& -1\\ 1& 1\\ 2& 10\end{array}$

The relation is _____, and ____ ordered pairs possible.

• A. a function; $8$
• B. not a function; $8$
• C. a function; $10$
  
• D. not a function; $10$

Answer 1

The correct option is B not a function; $8$

Detailed step-by-step solution:
Let’s write down all the combinations of inputs and outputs for the above table.
$(-3,4),(-2,-1),(0,5),(2,10),(-1,8),(3,0),(-3,-2),(-2,-1),(1,1),(2,10)$
Here, the points $(-2,-1)$ and $(2,10)$ are repeated twice.

$\Rightarrow$ On listing down all the unique combinations of inputs and outputs:
$(-3,4),(0,5),(2,10),(-1,8),(3,0),(-3,-2),(-2,-1),(1,1)$
So there are 8 unique order pairs possible.
Here for the input $-3,$ there are more than one output, $4$ and $-2.$
So it is not following the rules of function, which states that every input has to have a unique output.
Hence, the above input and output pairs are not representing a function.

So, option A is the correct answer.