Question

A relation is given below between $x$ and $y.$


Which of the following statements is correct about the graph?

• A. By removing the point $(0,5),$ the above relation will be a function.
• B. Above relation is not a function, because $-10$ is the output for the input $-3$ and $-2.$
• C. Above relation is a function, because $1$ and $5$ are the two outputs for the input $0.$
• D. By removing the point $(-2,-10),$ the above relation will be a function.

Answer 1

The correct option is A By removing the point $(0,5),$ the above relation will be a function.

Detailed step-by-step solution:
The point coordinates on the given graph are: $(-3,-10),(-2,-10),(-1,-5),(0,1),(0,5),(1,3),(2,10),(3,12)$
Here for the input $0,$ there are more than one output, $1$ and $5.$
So the given relation between the points is not a function.
Hence, the statement in option D is not true.

$\to$ By removing the point $(-2,-10)$ from the graph, the remaining points will be
$(-3,-10),(-1,-5),(0,1),(0,5),(1,3),(2,10),$ and $(3,12)$.
Still here for the input 0, there are more than one output, $1$ and $5.$
So the new relation between the points is not a function.
Hence, the statement given in option A is not true.

$\to$ By removing the point $(0,5)$ from the graph, the remaining points will be $(-3,-10),$ $(-2,-10),$ $(-1,-5),$ $(0,1),$ $(1,3),$ $(2,10),$ and $(3,12),$
Here, all the inputs have unique outputs.
So the new relation between the points is a function.
Hence, the statement given in option B is true.

$\to$ A relation cannot be qualified as a function, if one input has more than one output.
But if more than one input has the same output, then that can be considered as a function.
In option C, the reason for the relation not being a function is given as $“-10$ is the output for the input $-3$ and $-2”,$ which is not correct.
Hence, the statement given in option C is not true.

So, option B is the correct answer.