Question

Explain what the vertical line test is and how it is used.

Answer 1

✧ $\underline{ \underline{ \pink{\large{ \tt{E \: X \: P \: L\: A \: N \: A \: T \: I \: O \: N}}}}}:$

Part 1 :

☃ $\underline{ \large{ \sf{Vertical \: Line \: Test}}} :$ ⇾ All the relations are not functions. We can determine ( identify ) whether a relation is function or not by drawing a vertical line intersecting the graph of the relation. This is called the vertical line test.

• If the vertical line intersects the graph of a relation at one point , the relation is a function.
• If it cuts at more than one point , it is not a function. It means that if there are more points of the graph of a relation of a vertical line , same first component ( pre - image ) has more images ( second component ) which is not the function by definition.

( See the attached picture )

1. In the picture ' 1 ' , The vertical line ( dotted line ) cuts the graph at one point ( P ). Thus the graph represents a function.
2. In the picture ' 2 ' , The vertical line ( dotted line ) cuts the graph at two points P & Q. So, the graph does not represent a function.

Part 2 :

☂ The set of all the images of the elements of domain under the function ' f ' is called the range of a function. In other words , the set of second components of a function is called range. We are given the function :

• {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}

The above numbers [ in bold ] are the range of given function. Now, If we arrange these numbers in ascending order, we get ( -9 , -3 , 0 , 5 , 7 ).

Hence , Choice B [ {y | y = –9, –3, 0, 5, 7} ] is correct.

♕ Hope I helped! ♡

☄ Have a wonderful day / night ! ☼

✎ $\underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}$ ☥

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