How to find if y is a function of x

Asked by admin @ 28/10/2021 in Mathematics viewed by 371 People

Select all of the following graphs which represent y as a function of x

Answered by admin @ 28/10/2021

To solve this question, we use the definition of a function, which includes that:

For each value of x, there is only one possible value of y.
As a graph, if we trace a vertical line, it cannot cross more than one point of the function.

Doing this, we get that the graphics which represents functions are: a, b, d and e.

Graphic a:

Constant line, for each value of x, only one value of y, so yes, it is a function.

Graphic b:

For each value of x, only one value of y, so yes, it is a function.

Graphic c:

For values of x between -4 and 0, there are more than 1 value of y, thus, it is not a function. Using a vertical line, as in the picture at the end of the question, you can see that it crosses more than one point of the function.

Graphic d:

For each value of x, only one value of y, so yes, it is a function.

Graphic e:

For each value of x, only one value of y, so yes, it is a function.

Graphic f:

For values of x between -4 and 0, there are more than 1 value of y, thus, it is not a function. Using the vertical line test, as for option c, you can verify the same thing.

Thus:

Graphics a,b, d and e represent functions.

A similar example is given at brainly.com/question/17267403

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