Question

Which of the following relations represents a function?

• A.
• B. $\begin{array}{cccccc}\left(x\right)& -1& 0& 1& -2& 0\\ \left(y\right)& 5& 0& -5& 10& 10\end{array}$
• C. $(-10,5),(-8,5),(-6,5),(-4,5),(-2,5),(0,5)$
• D.

Answer 1

The correct option is C $(-10,5),(-8,5),(-6,5),(-4,5),(-2,5),(0,5)$

Detailed step-by-step solution:

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 a relation will not qualify as a function.

Let’s discuss the relations one-by-one here.

$\to$ According to the graph, the input and output pairs are: $(-3,1),(-2,-1),(-1,2),$
(0, -2), (1, 3), (2, 1), (2, -3), (3, -1)
Here, the input $“2”$ has more than one output.
It is not following the conditions of a function.
So, the relation in option A does not represent a function.

$\to$ According to the table, the input and output order pairs are: $(-1,5),(0,0),(1,-5),$ $(-2,10),(0,10)$
Here, the input “0” has more than one output.
It is not following the conditions of a function.
So, the relation in option B does not represent a function.

$\to$ In the given relation, from set $x$ to set $y,$ the input and output pairs are: $(5,11),(6,13),(-7,-13),(5,9),(-6,-11),(7,15)$
Here, the input $“5”$ has more than one output.
It is not following the conditions of a function.
So the relation in option C does not represent a function.

$\to$ The given input and output point pairs are: $(-10,5),(-8,5),(-6,5),(-4,5),(-2,5),(0,5)$
Here, for each input, there is a unique output.
It is following the conditions of a function.
So the relation in option D is a function.

So, option D is the correct answer.