Answer:
<em>Graph given in </em><em>Question 18</em><em> is </em><em>a function</em><em> and the graph given in </em><em>Question 19</em><em> is </em><em>not a function</em><em>. Just check the </em><em>attached figure.</em>
Step-by-step explanation:
From the given graph of a relation, it is easy to establish whether the given relation is a function or not. In order to determine the nature of the relation, there is vertical line test. This test can be done by drawing any vertical line crossing the graph of the given relation. This vertical line has a constant x -a line having constant x.
If this vertical line crosses the graph multiple times, then we can determine that the relation would not be a function. It means the graph contains multiple values of y for a single value of x. This violates the condition of a relation to be a function. Hence, the relation would not be a graph.
But, if the vertical line crosses the graph only one time, then we can determine that the given relation would be a function. It means the graph does not contain multiple values of y for a single value of x.
<em>Solution of the Graph given in Question 18:</em>
From the given graph of a relation, that sounds like a circle. It means the relation shown in current graph is not a function. The reason is simple. If we draw a vertical line, then the line would cross the graph twice. Hence, the given graph of a relation is not a function.
Just check that the value of x=1 will have two y values i.e (1, 5) and (1, -1). Also, at origin, for a value of x = 0, there are multiple values of y. Hence, the graph is not a not a function, but just a relation. Just check the <em>attached figure.</em>
<em>Solution of the Graph given in Question 19:</em>
From the given graph of a relation, it is clear that the graph is a function. The reason is simple. If we draw a vertical line, then the line would cross the graph only one time. Hence, the given graph of a relation is a function.
Just check that the points (0, 0), (2, 3), (-1, 3), (-3, 3) and (1, -3) all make a function as each input value yields an exactly one output function. Hence, the given graph of the relation is a graph. Just check the <em>attached figure.</em>
<em>Keywords: function, relation, ordered pairs, graph, vertical line test</em>
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