TI 83/84 Graphing Calculator Activity

by Tia Price

Introduction

In mathematics, a change in the size or position of a figure or graph is called a transformation. Types of transformations are translations (horizontal or vertical shifts), reflections, dilations, stretches, shrinks and rotations. By transforming a parent function, or building-block function, you can create infinitely many new functions. The sooner students can recognize these transformations, the easier their study of families of functions will be.

Let’s start with the most basic function: The Linear Function

The Parent Function

y = x

The first function Algebra students study

is the linear function: .

The students should recognize patterns in

the linear function. What happens as m gets

larger or smaller? What happens as b changes

value? The APPS program, Transformation

Graphing, has now made this investigation a

lot easier.

Let’s discover the effect of m and b in the linear function. Go to APPS menu and arrow up once, taking you to the bottom of the APPLICATIONS menu. Hit enter and then enter again. Now go to your Y= screen and notice how it has been altered.

Examining changes in A

  1. Type in AX+B for .
  2. Now press ZOOM 6 to give us a “standard window”.

Startwith the identity function: type in 1 for A (slope of 1) and 0 for B (y-intercept of 0). Using the up and down arrow keys, you can move the variable A to variable B, and you can either type in the value you would like or use the left and right arrow keys to increase or decease.

  1. Be sure your cursor is highlighted on.
  2. Using the right arrow key, watch the graph as the value for A increases as you press the right arrow key.
  3. Now press the left arrow key and watch the changes in the graph as A decreases. Note the graph at, then , and so on.

Explain what is happening to the graph as you keep the value of B constant and increase the value of A. ______

Explain what is happening to the graph as you keep the value of B constant and decrease the value of A. ______

Examining changes in B

  1. Next type in 1for A and 1 for B.
  2. Be sure your cursor is highlighted on.
  3. Using the right arrow key, watch the graph as the value for B increases as you press the right arrow key.
  4. Now press the left arrow key and watch the changes in the graph as B decreases.

Explain what is happening to the graph as you keep the value of A constant and increase the value of B. ______

Explain what is happening to the graph as you keep the value of A constant and decrease the value of B. ______

Continue to experiment with other values for A and B until you can predict how the graph will look for those values.