Question

The following table shows the values of y for different values of x:

Answer 1

Answer:

Option B. It represents a nonlinear function because its points are not on a straight line.

Step-by-step explanation:

Let

$A(0,0),B(1,1),C(2,4)$

we know that

If point A,B and C are on a straight line

then

The slope of AB must be equal to the slope of AC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Find the slope AB

$A(0,0),B(1,1)$

substitute in the formula

$m_A_B=\frac{1-0}{1-0}=1$

Find the slope AC

$A(0,0),C(2,4)$

substitute in the formula

$m_A_C=\frac{4-0}{2-0}=2$

so

$m_A_B\neq m_A_C$

Points A, B and C are not on a straight line

therefore

It represents a nonlinear function because its points are not on a straight line

Answer 2

Answer:

Option B) It represents a nonlinear function because its points are not on a straight line.    

Step-by-step explanation:

We are given the following information in the question:

Different values of y for different values of x:

x:    0    1    2

y:    0    1    4

The attached images shows the given points plot on a graph.

From the graph it can be observed that the points does not lie on a straight line but on a curved line.

Since the points does not lie on a straight line, thus it is not a linear function.

Thus, it is a non linear function.

Thus, Option B) is the correct answer.

It represents a nonlinear function because its points are not on a straight line.