Answer:
1. Identify 2 points
2.Calculate the Change in Y and X Values
3.Compute the Average Rate of Change (Slope)
Explanation:
Identify Two Points: First, identify two points on the graph. These points should lie on the function curve. You can either read the coordinates directly from the graph or use the function’s equation to find the corresponding values.
Calculate the Change in Y and X Values: Let the coordinates of the two points be ((x_1, y_1)) and ((x_2, y_2)). The change in the output value is given by (y_2 - y_1), and the change in the input value is given by (x_2 - x_1).
Compute the Average Rate of Change (Slope): Use the formula:
{y_2 - y_1}{x_2 - x_1}
If the value is positive, it indicates an increasing function.
If the value is negative, it suggests a decreasing function.
Remember that the rate of change provides insights into how one quantity changes relative to another. For linear functions, the rate of change is constant (the slope of the line). However, for nonlinear functions, the rate can vary at different intervals. Analyzing rates of change helps us understand relationships between variables in equations and graphs.
