AP Precalculus Section 1.13 Example: TI-84+ Calculator Word Problem (Maximizing & Restricted Domain)

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 maximum value of a function on a given interval using a TI-84+ calculator, you can use the following 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 where you want to find the maximum value.

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

4. **Locate the Maximum Point:**
- Press the `2nd` button.
- Press the `TRACE` button.
- Choose option `4: maximum` by scrolling down or pressing the `4` key.
- Enter the left and right bounds of the interval where you expect the maximum to occur. This defines the interval for the calculator to search.
- Press `ENTER` to execute.

5. **Read the Maximum Point:**
- The calculator will display the coordinates of the maximum point as (x, y).
- Note the x-coordinate (the value of x where the maximum occurs) and the y-coordinate (the maximum value of the function).

Alternatively, you can use the `2nd` and `CALC` buttons to find the maximum value:

1. Press the `2nd` button.
2. Press the `CALC` button.
3. Choose option `3: maximum` from the menu.
4. Enter the left and right bounds of the interval.
5. Press `ENTER` to execute.

These steps will help you find the maximum value of a function on a given interval using your TI-84+ calculator. Make sure to set an appropriate viewing window to ensure that you capture the relevant part of the graph.

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

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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