Answer:
The rate of change of function 2 is 4 more than that of function 1.
Step-by-step explanation:
Given:
A graph of a function 1 having points [tex](0,3)\textrm{ and }(4,3)[/tex]
An equation of the line for function 2 as [tex]y=4x+1[/tex]
Now, rate of change is nothing but the slope of the lines.
Slope of function 1 is given as:
[tex]m_{1}=\frac{y_2-y_1}{x_2-x_1}\\m_{1}=\frac{3-3}{4-0}=0[/tex]
Slope of line of function 2 is equal to the coefficient of [tex]x[/tex] in the equation.
Therefore, [tex]m_2=4[/tex] as coefficient of [tex]x[/tex] is 4.
Now, difference in the rate of change of both the functions is:
[tex]m_2-m_1=4-0=4\\m_2=m_1+4[/tex]
Therefore, the rate of change of function 2 is 4 more than that of function 1.
