AP Precalculus Section 1.13 Example: TI-84+ Calculator Word Problem on Average 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!

To find the average rate of change of a function over a given interval using a TI-84+ calculator, you can follow these steps:

1. **Enter the Function:**
- Turn on your TI-84+ calculator.
- Press the `Y=` button to enter the "Y=" editor.
- Enter the function using the "X" variable. For example, if your function is \( f(x) = 2x^2 + 3x - 5 \), you would enter it as `Y1 = 2X^2 + 3X - 5`.

2. **Set the Window:**
- Press the `WINDOW` button to set the viewing window for your graph.
- Make sure the X values are set to cover the desired interval. For example, if the interval is [a, b], set the X values accordingly.

3. **Graph the Function:**
- Press the `GRAPH` button to plot the function on the graph.

4. **Trace to Find Endpoints of the Interval:**
- Press the `TRACE` button.
- Move the cursor to one endpoint of the interval using the arrow keys.
- Note the x-coordinate of the point.

5. **Repeat for the Other Endpoint:**
- Move the cursor to the other endpoint of the interval using the arrow keys.
- Note the x-coordinate of this point as well.

6. **Calculate the Average Rate of Change:**
- Subtract the initial x-coordinate from the final x-coordinate to find the change in x (\( \Delta x \)).
- Use the function values at the two endpoints to find the corresponding y-coordinates, let's call them \( f(a) \) and \( f(b) \).
- Calculate the average rate of change using the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{\Delta x} \]

7. **Use the Calculator's Built-in Function:**
- Alternatively, some TI-84+ calculators have a built-in feature for finding the average rate of change. To access it:
- Press the `2nd` button.
- Press the `STAT` button.
- Scroll right to the `CALC` menu.
- Choose "5: LinReg(ax+b)" and press `ENTER`.
- Input the two endpoints of the interval.
- The calculator will display the average rate of change.

Using these steps, you can find the average rate of change for a given function over a specified interval using the TI-84+ calculator.

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
Norristown, Pa

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