Question

# Given an example of a non-linear function in table form.

X | |||||

Y |

Hint:

### A non linear function has a slope which is not constant between all the points. So we make the table in such a way that the slope between the first two points and the next two points are unequal. This will give a non linear function.

## The correct answer is: not a linear function.

*Step by step solution:*

We take the values of x to 0, 1, 2, 3 and 4.

First, we take the value as y = 0 for x = 0

Next, we assume y = 2 for x = 1

The slope between two points (a, b) and (c, d) is given by

We take the above two points to be

(a, b) = (0, 0) and (c, d) = (1, 2)

Calculating the slope, we have

Thus, the slope between first two points = 2

Next, for x = 2, we choose the value of y in such a way that the slope between the second point and this point is not equal to 2.

For x = 2, we choose, y = 7

Slope between two points (a, b) and (c, d) is given by

We take the above two points to be

(a, b) = (1, 2) and (c, d) = (2, 7)

Calculating the slope, we have

For the rest of the values of x, we can choose any arbitrary value of y.

We choose,

For x = 3, y = 4

For x = 4, y = 9

Finally, the table becomes

x

0

1

2

3

4

y

0

2

7

4

9

This is an example of a non linear function.

We know that the graph of a non linear function is not a straight line.

So, we can plot the above ordered pairs to verify that the graph of the above points is not a straight line and hence not a linear function.

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