Question

Which table represents a nonlinear function? x y 2 -9 4 1 6 11 x y 2 -14 4 -16 6 -18 x y 2 0 4 6 6 16 x y 2 -9 4 -6 6 -3

Answer 1

The Third one, Y jumps from 0 to 6 then 16

Answer 2

Answer:  The third table represents a nonlinear function

x  y

2  0

4  6

6 16

Step-by-step explanation:

We know that for a nonlinear function, the rate of change of y is not constant w.r.t x.

The rate of change of y w.r.t. x is given by :-

$\dfrac{\text{Change in y}}{\text{Change in x}}$

For Table 1.

The rate of change of function is given by :_

$\dfrac{1-(-9)}{4-2}=\dfrac{10}{2}=5$

$\dfrac{11-1}{6-4}=\dfrac{10}{2}=5$

Thus , the rate of change is constant through out the function, hence it is not representing a nonlinear function.

For Table 2.

The rate of change of function is given by :_

$\dfrac{-16-(-14)}{4-2}=\dfrac{-2}{2}=-1$

$\dfrac{-18-(-16)}{6-4}=\dfrac{-2}{2}=-1$

Thus , the rate of change is constant through out the function, hence it is not representing a nonlinear function.

For Table 3.

The rate of change of function is given by :_

$\dfrac{6-0}{4-2}=\dfrac{6}{2}=3$

$\dfrac{16-6}{6-4}=\dfrac{10}{2}=5$

Thus , the rate of change is not constant through out the function, hence it is representing a nonlinear function.

For Table 4.

The rate of change of function is given by :_

$\dfrac{-6-(-9)}{4-2}=\dfrac{3}{2}$

$\dfrac{-3-(-6)}{6-4}=\dfrac{3}{2}$

Thus , the rate of change is constant through out the function, hence it is not representing a nonlinear function.