Answer:
Option B. It represents a nonlinear function because its points are not on a straight line.
Step-by-step explanation:
Let
[tex]A(0,0),B(1,1),C(2,4)[/tex]
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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Find the slope AB
[tex]A(0,0),B(1,1)[/tex]
substitute in the formula
[tex]m_A_B=\frac{1-0}{1-0}=1[/tex]
Find the slope AC
[tex]A(0,0),C(2,4)[/tex]
substitute in the formula
[tex]m_A_C=\frac{4-0}{2-0}=2[/tex]
so
[tex]m_A_B\neq m_A_C[/tex]
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
