Math Problem Statement

−3 18 0 9 2 3 5 −6 7 −12 (a) Find the rate of change of f.

Solution

To calculate the rate of change of a function ff, we need to know the formula:

Rate of change=Change in yChange in x=f(x2)f(x1)x2x1\text{Rate of change} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

From the numbers you provided, it seems like a set of data points, but I need clarification on how these values are organized. Typically, you'd have pairs like (x1,y1),(x2,y2),(x_1, y_1), (x_2, y_2), \ldots.

Could you confirm whether these are the xx-values and the corresponding f(x)f(x)-values, or if you want me to assume any particular structure for them?

Once I know that, I can compute the rate of change for you.

Let me know if you'd like further details! Here are some related questions:

  1. What is the slope of a linear function?
  2. How do you calculate the rate of change between two points on a line?
  3. What is the difference between average rate of change and instantaneous rate of change?
  4. How can the rate of change be interpreted in real-world contexts (e.g., speed)?
  5. How would you calculate the rate of change for a quadratic function?

Tip: The rate of change is equivalent to the slope of the line when the data points form a straight line.

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Math Problem Analysis

Mathematical Concepts

Rate of Change
Slope
Linear Functions

Formulas

Rate of Change = (f(x2) - f(x1)) / (x2 - x1)

Theorems

Slope formula
Average rate of change

Suitable Grade Level

Grades 7-9