AP Precalculus Section 1.14 Example: Word Problem on Rate of Change

Random AP Precalculus Problems (I found on the Internet). These are not official AP Collegeboard examples, but they will definitely get the job done!

You can use the average rate of change formula to find the average rate of change on an interval when given a table of values. Here's how to do it:

1. Determine the interval: Identify the specific interval (range of x-values) over which you want to calculate the average rate of change.

2. Identify the endpoints: Determine the x-values corresponding to the starting and ending points of the interval. Let's call them "x1" and "x2."

3. Find the corresponding function values: Look up the corresponding y-values (function values) for both "x1" and "x2" in the table.

4. Apply the formula: Use the average rate of change formula:
Average Rate of Change = (Change in y) / (Change in x)

Calculate the change in y by subtracting the y-value at "x1" from the y-value at "x2," and calculate the change in x by subtracting "x1" from "x2."

5. Calculate the average rate of change: Divide the change in y by the change in x to find the average rate of change over the specified interval.

Here's the formula again with specific values:
Average Rate of Change = (y2 - y1) / (x2 - x1)

By following these steps and using the formula, you can calculate the average rate of change for a given interval using a table of values.

The Topics covered in AP Precalculus are...

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application
2.1 Change in Arithmetic and Geometric Sequences
2.2 Change in Linear and Exponential Functions
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Context and Data Modeling
2.6 Competing Function Model Validation
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation
2.13 Exponential and Logarithmic Equations and Inequalities
2.14 Logarithmic Function Context and Data Modeling
2.15 Semi-log Plots
3.1 Periodic Phenomena
3.2 Sine, Cosine, and Tangent
3.3 Sine and Cosine Function Values
3.4 Sine and Cosine Function Graphs
3.5 Sinusoidal Functions
3.6 Sinusoidal Function Transformations
3.7 Sinusoidal Function Context and Data Modeling
3.8 The Tangent Function
3.9 Inverse Trigonometric Functions
3.10 Trigonometric Equations and Inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.12 Equivalent Representations of Trigonometric Functions
3.13 Trigonometry and Polar Coordinates
3.14 Polar Function Graphs
3.15 Rates of Change in Polar Functions

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Nick Perich
Norristown Area High School
Norristown Area School District
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