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)](/tpl/images/0294/1355/b2e6e.png)
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}](/tpl/images/0294/1355/baca9.png)
Find the slope AB
![A(0,0),B(1,1)](/tpl/images/0294/1355/b1641.png)
substitute in the formula
![m_A_B=\frac{1-0}{1-0}=1](/tpl/images/0294/1355/f104f.png)
Find the slope AC
![A(0,0),C(2,4)](/tpl/images/0294/1355/5c4d6.png)
substitute in the formula
![m_A_C=\frac{4-0}{2-0}=2](/tpl/images/0294/1355/33708.png)
so
![m_A_B\neq m_A_C](/tpl/images/0294/1355/dedfd.png)
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