The function C has the greatest initial value, and the function B has the greatest rate of change
Linear function
A linear function is a function whose value changes at a constant rate.
A linear function is represented as:
[tex]y = mx + c[/tex]
Where
- m represents the rate
- c represents the initial value, or the value of the function, when x = 0
Initial values
The initial value of function A is 0.
This is so because y = 0, when x = 0
The initial value of function B is -1
This is so because the value of function y = 3x - 1 is -1, when x = 0
From the graph, the initial value of function C is 2
Hence, the function C has the greatest initial value
Rate of change
Rate of change is calculated as:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, the rate of change of function A is calculated as follows:
[tex]m = \frac{5 - 0}{2-0}[/tex]
[tex]m = \frac{5 }{2}[/tex]
[tex]m = 2.5[/tex]
The rate of change of function A is 2.5
The rate of change of function B is 3.
The rate of change of function C is calculated as follows:
[tex]m = \frac{3 - 2}{3-0}[/tex]
[tex]m = \frac{1}{3}[/tex]
The rate of change of function C is 1/3
Hence, the function B has the greatest rate of change
Read more about linear functions at:
https://brainly.com/question/14323743
