Average rate of change (AR. c)
The average rate of change (ARC) in mathematics refers to the average rate at which one quantity changes with respect to another quantity over a specific interval or range
The average rate of change (ARC) in mathematics refers to the average rate at which one quantity changes with respect to another quantity over a specific interval or range. It is calculated by dividing the difference in the values of the two quantities by the difference in their corresponding units.
To find the average rate of change between two points on a function or a graph, follow these steps:
1. Identify the given two points on the graph or function. Let’s call them (x1, y1) and (x2, y2), where x1 and x2 are the values of the independent variable (usually represented on the x-axis) and y1 and y2 are the corresponding values of the dependent variable (usually represented on the y-axis).
2. Determine the change in the dependent variable. This is done by subtracting the initial value of the dependent variable from the final value. It can be calculated as Δy = y2 – y1.
3. Calculate the change in the independent variable. This is done by subtracting the initial value of the independent variable from the final value. It can be calculated as Δx = x2 – x1.
4. Finally, calculate the average rate of change by dividing the change in the dependent variable (Δy) by the change in the independent variable (Δx). It can be expressed as ARC = Δy/Δx.
The result of the average rate of change is a numerical value that represents the average rate at which the dependent variable changes for each unit change in the independent variable.
For example, let’s consider a linear function given by the equation y = 2x + 3. To find the average rate of change between the points (1, 5) and (4, 11):
Δy = y2 – y1 = 11 – 5 = 6
Δx = x2 – x1 = 4 – 1 = 3
ARC = Δy/Δx = 6/3 = 2
Therefore, the average rate of change of the function y = 2x + 3 between the points (1, 5) and (4, 11) is 2. This means that for every unit increase in the independent variable (x), the dependent variable (y) increases by an average of 2 units.
Understanding the concept of average rate of change is important in various mathematical applications, such as analyzing the speed of an object, determining the growth or decline of a quantity over time, and studying the slope or steepness of a graph.
More Answers:
Understanding Even and Odd Functions in Mathematics: Properties and ExamplesUnderstanding Increasing Functions: Definition, Examples, and Properties
Understanding Decreasing Functions: Explained with Examples and Graphical Representations