given a graph of a function, explain how to find the rate of change and how to determine whether it is a…

given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

Answer

Brief Explanations:

  • Rate of Change:
    • Select two distinct points ((x_1,y_1)) and ((x_2,y_2)) on the graph. The rate of change (slope) is calculated using the formula (m=\frac{y_2 - y_1}{x_2 - x_1}).
  • Linear vs Non - linear:
    • A linear function has a constant rate of change. So, if the rate of change (slope) calculated between any two pairs of points on the graph is the same, the function is linear.
    • A non - linear function has a non - constant rate of change. That is, when you calculate the rate of change (slope) between different pairs of points on the graph, you get different values.

Answer:

To find the rate of change, use the formula (m=\frac{y_2 - y_1}{x_2 - x_1}) for two points ((x_1,y_1)) and ((x_2,y_2)) on the graph. A function is linear if the rate of change is constant (same for any two points), and non - linear if the rate of change is not constant.