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

What is the range of the given function?

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

{x | x = –5, –4, –2, 0, 2}
{y | y = –9, –3, 0, 5, 7}
{x | x = –9, –5, –4, –3, –2, 0, 2, 5, 7}
{y | y = –9, –5, –4, –3, –2, 0, 2, 5, 7}

☃ [tex] \underline{ \large{ \sf{Vertical \: Line \: Test}}} : [/tex] ⇾ 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 )

In the picture ' 1 ' , The vertical line ( dotted line ) cuts the graph at one point ( P ). Thus the graph represents a function.
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 ! ☼

✎ [tex] \underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}[/tex] ☥

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baumeralexa baumeralexa · Answer 2 · 2021-08-21T03:20:29+02:00

baumeralexa baumeralexa

21-08-2021

Sample Response:

The vertical line test is a way to determine if a relation is a function. This test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function because two different outputs have the same input.

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