Maths-

General

Easy

Question

# How can you determine whether the relationship between side length and area is a function?

If it is a function, say whether it is linear or non linear function ?

Hint:

### An equation of the form y=f(x) is called a function if there is a unique value of y for every value of x. In other words, we should get exactly one value of y for every value is x we put in the equation. Recall, that a function is linear if the graph of the function is a straight line.

## The correct answer is: a linear function

*Step by step solution:*

Let us denote the length by x.

Let us denote the area by y.

From the table, we can observe that there is a different and unique value of y for every x.

This gives that the given relationship is a function.

Next, we draw the graph of the function to check its linearity.

We construct the following table

x

0

1

2

3

4

5

y

0

1

4

9

16

25

We plot the above points in the following graph.

Clearly, the graph is not a straight line. Hence the given relationship between length and area is not a linear function.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.

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