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Debora [2.8K]
3 years ago
9

Which is a counterexample for the conditional statement shown?

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
7 0

Answer: First Option

<em>The points have the same x-coordinate value.</em>

Step-by-step explanation:

By definition, a relation is considered a function if and only if for each input value x there exists <u><em>only one </em></u>output value y.

So, the only way that the line that connects two points in the coordinate plane is not a function, is that these two points have the same coordinate for x.

For example, suppose you have the points (2, 5) and (2, 8) and draw a line that connects these two points.

The line will be parallel to the y axis.

Note that the value of x is the same x = 2. But when x = 2 then y = 5 and y = 8.

There <u><em>are two output</em></u><em> </em>values (y = 8, y = 5) for the same input value x = 2.

In fact all the vertical lines parallel to the y-axis have infinite output values "y" for a single input value x. Therefore, they can not be defined as a function.

<u>Then the correct option is: </u>

<em>The points have the same x-coordinate value.</em>

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