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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