Question

Which of the following statements is not true about the above four graphs?

Answer 1

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 consider all the graphs one-by-one.

Graph 1: In this graph, the input and output pairs are \((-3, 1), (-2, 1), (-1, 1), (0, 1),\)
\((1, 1), (2, 1),\) and \((3, 1).\)
Here each input has a unique output and for all the inputs, the output is the same, i.e., \(1.\)
It is following the conditions of a function.
Hence, Graph \(1\) is a function.
\(\Rightarrow\) Option C is true.

Graph 2: In this graph, the input and output pairs are \((-2, -3), (-2, -2), (-2, -1),\) \((-2, 0), (-2, 1), (-2, 2),\) and \((-2, 3).\)
Here for one input, there are more than one outputs.
This is not following the conditions of a function.
Hence, Graph 2 is not a function.
\(\Rightarrow\) Option D is true.

Graph 3: In this graph, the input and output pairs are \((-3, -3), (-2, -2), (-1, -1),\)
\((0, 0), (1, 1), (2, 2),\) and \((3, 3).\)
Here, each input has a unique output.
It is following the conditions of a function.
Hence, Graph \(3\) is a function.
\(\Rightarrow\) Option B is true.

Graph 4: In this graph, the input and output pairs are \((-1, 2), (0, 2), (1, 2), (2, 1), (2, 0), (2, -1), (1, -2), (0, -2), (-1, -2), (-2, -1), (-2, 0), (-2, 1)\)
Here in some cases, for a single input, there are more than one outputs.
It is not following the conditions of a function.
Hence, Graph \(4\) is not a function.
\(\Rightarrow\) Option A is not true.

So, option A is the correct answer.