1. How to Find Domain on TI-83

The domain of a function is the set of all possible input values. The range of a function is the set of all possible output values. Finding the domain and range of a function is an important step in understanding the function. There are a few different ways to find the domain and range of a function, depending on the type of function.

Here are a few simple tips for evaluating the domain of a function using a TI-83 graphing calculator:

First, enter the function into the calculator. To do this, press the “y=” button and then enter the function using the calculator’s keypad. For example, to enter the function y = x^2, you would press “y=”, then “x”, then “^”, and then “2”.
Once the function is entered, press the “graph” button to see the graph of the function. The graph will help you to visualize the domain and range of the function.
To find the domain of the function, look at the x-values of the points on the graph. The domain is the set of all possible x-values for which the function is defined. In other words, the domain is the set of all x-values for which the graph exists.
For example, consider the function y = x^2. The graph of this function is a parabola that opens up. The parabola exists for all real numbers, so the domain of the function is all real numbers. In interval notation, we would write the domain as (-∞, ∞).

Accessing the Home Screen

The Ti-83 graphing calculator is a powerful tool that can be used for a variety of mathematical operations, from basic arithmetic to advanced calculus. One of the most important features of the Ti-83 is its home screen, which is where you will enter and execute commands. The home screen is divided into two parts: the main display and the status line. The main display is where you will enter and execute commands, while the status line displays information about the current state of the calculator.

To access the home screen, you will need to press the [2nd] key followed by the [MODE] key. This will take you to the Main Menu. From the Main Menu, use the arrow keys to navigate to the Home Screen option and then press the [ENTER] key. You will now be on the home screen.

Here is a summary of the steps on how to access the home screen:

Step	Action
1	Press the [2nd] key followed by the [MODE] key to access the Main Menu.
2	Use the arrow keys to navigate to the Home Screen option.
3	Press the [ENTER] key to select the Home Screen option.

Navigating the Menu

The TI-83 calculator features a user-friendly menu interface that enables easy navigation and access to various functions and applications. To navigate through the menu, follow these steps:

Press the MENU key to open the main menu.
Use the arrow keys to scroll through the menu options, which are categorized into submenus such as “Math,” “List,” and “Program.”
Press ENTER to select the desired submenu.
Continue navigating and selecting items within the submenus using the arrow keys and ENTER key.
To return to the previous menu level, press the ESC key.
To exit the menu and return to the home screen, press the QUIT key.

Selecting the “Vars” Option

3. Access the “Vars” Menu:

To access the “Vars” menu, press the blue “vars” key located on the far left of the calculator. This key will display a menu with various options, including the “Y-Vars” and “Window” submenus. In order to find the domain of a function, we will need to access the “Window” submenu.

Press the “vars” key

Access the “Vars” menu

4. Enter the “Window” Submenu:

To enter the “Window” submenu, use the arrow keys to navigate to the “Window” option and press the “enter” key. This will display the “Window” settings, including the “Xmin” and “Xmax” values, which define the domain of the function.

Navigate to the “Window” option

Press the “enter” key

5. Identify the “Xmin” and “Xmax” Values:

The “Xmin” and “Xmax” values define the left and right endpoints of the domain, respectively. To find the domain of the function, simply read these values from the “Window” settings. For example, if the “Xmin” value is -5 and the “Xmax” value is 10, the domain of the function is: [-5, 10].

Read the “Xmin” and “Xmax” values

Determine the domain of the function

Entering Domain Equations

To enter domain equations into a TI-83 calculator, follow these steps:

1. Press the “Y=” key.

This will bring up the equation editor.

2. Enter the equation for the lower bound of the domain.

For example, if the lower bound is x = 2, enter “2”.

3. Press the “],” key.

This will insert a comma into the equation.

4. Enter the equation for the upper bound of the domain.

For example, if the upper bound is x = 5, enter “5”.

5. Press the “ENTER” key.

This will store the domain equation into the calculator. To view the domain equation, press the “2nd” key followed by the “Y=” key. The domain equation will be displayed on the calculator screen.

Example	Domain Equation
x ≥ 2	2,
x ≤ 5	,5
2 ≤ x ≤ 5	2,5

Viewing the Graph

To view the graph of the function you entered, press the “GRAPH” button located at the top right corner of the calculator. The graph will appear on the calculator’s screen, plotted over the viewing rectangle. You can use the arrow keys to navigate around the graph and zoom in or out by pressing the “ZOOM” button and selecting the desired zoom option.

How to find the domain of a graph

To find the domain of a graph, follow these steps:

Press the “2nd” button and then the “CALC” button to access the calculator’s “CALC” menu.
Select option 5: “zero.”
Enter the lower bound of the viewing rectangle (the “left” value) and press the “ENTER” button.
Enter the upper bound of the viewing rectangle (the “right” value) and press the “ENTER” button.
The calculator will display a table showing the x-values of the zero crossings (if any) within the specified viewing rectangle.
To find the minimum and maximum values of the function within the viewing rectangle, press the “2nd” button and then the “VARS” button to access the calculator’s “VARS” menu.

Select option 5: “statistics.”

Press	To
“1: Edit”	Edit the list of data points
“2: Sort A”	Sort the data in ascending order
“3: Sort D”	Sort the data in descending order
“4: ClrList”	Clear the list of data points
“5: SetUpEditor”	Set up the data editor

Select option 2: “MinMax,” and the calculator will display a table showing the minimum and maximum values of the function within the specified viewing rectangle.

Advanced Domain Manipulation

Once you have found the domain of a function, you can manipulate it in a variety of ways.

Restricting the Domain

You can restrict the domain of a function by imposing conditions on the input values. For example, the domain of the function f(x) = 1/x is all real numbers except 0. However, you could restrict the domain to only positive numbers or only negative numbers.

Enlarging the Domain

You can also enlarge the domain of a function by removing conditions on the input values. For example, the domain of the function g(x) = √(x – 1) is all real numbers greater than or equal to 1. However, you could enlarge the domain to include all real numbers by removing the condition x ≥ 1.

Combining Domains

You can combine the domains of two or more functions to create a new domain. For example, if you have the functions f(x) = x² and g(x) = 1/x, you could combine their domains to create the domain x ≠ 0.

Intersecting Domains

You can also intersect the domains of two or more functions to create a new domain. For example, if you have the functions f(x) = x² and g(x) = √(x – 1), you could intersect their domains to create the domain x ≥ 1.

Exchanging Domains

You can exchange the domains of two functions to create two new functions. For example, if you have the functions f(x) = x² and g(x) = 1/x, you could exchange their domains to create the functions f'(x) = 1/x and g'(x) = x².

Shifting the Domain

You can shift the domain of a function to the left or right by adding or subtracting a constant. For example, the domain of the function f(x) = x² is all real numbers. However, you could shift the domain to the left by 1 by adding 1 to the input: f(x + 1) = (x + 1)².

Stretching the Domain

You can stretch the domain of a function by multiplying the input by a constant. For example, the domain of the function f(x) = x² is all real numbers. However, you could stretch the domain by 2 by multiplying the input by 2: f(2x) = (2x)².

Shrinking the Domain

You can shrink the domain of a function by dividing the input by a constant. For example, the domain of the function f(x) = x² is all real numbers. However, you could shrink the domain by 2 by dividing the input by 2: f(x/2) = (x/2)².

Reflecting the Domain

You can reflect the domain of a function over the x-axis by negating the input. For example, the domain of the function f(x) = x² is all real numbers. However, you could reflect the domain over the x-axis by negating the input: f(-x) = (-x)².

Combining Transformations

You can combine any of the above transformations to create more complex domain manipulations. For example, you could shift the domain of the function f(x) = x² to the left by 1, stretch the domain by 2, and reflect the domain over the x-axis to create the function f(-2x + 1) = (-2x + 1)².

Domain Manipulation	Example
Restricting the Domain	f(x) = 1/x, domain: all real numbers except 0
Enlarging the Domain	g(x) = √(x – 1), domain: all real numbers greater than or equal to 1
Combining Domains	f(x) = x², g(x) = 1/x, domain: x ≠ 0
Intersecting Domains	f(x) = x², g(x) = √(x – 1), domain: x ≥ 1
Exchanging Domains	f(x) = x², g(x) = 1/x, f'(x) = 1/x, g'(x) = x²
Shifting the Domain	f(x) = x², f(x + 1) = (x + 1)²
Stretching the Domain	f(x) = x², f(2x) = (2x)²
Shrinking the Domain	f(x) = x², f(x/2) = (x/2)²
Reflecting the Domain	f(x) = x², f(-x) = (-x)²
Combining Transformations	f(x) = x², f(-2x + 1) = (-2x + 1)²

How to Find Domain on TI-83

The domain of a function is the set of all possible input values for which the function is defined. To find the domain of a function on a TI-83 calculator, follow these steps:

Enter the function into the calculator in the Y= editor.
Press the [2nd] and then the [CALC] key to access the Calculate menu.
Select the "zero" option from the Calculate menu.
Enter the lower bound of the domain you want to find and press [ENTER].
Enter the upper bound of the domain you want to find and press [ENTER].
The calculator will display the domain of the function in the form [x, y], where x is the lower bound and y is the upper bound.