Using Multiple Representations and

the Graphing Calculator

Adapted from "Representation as a Vehicle for Solving and Communicating" by R, Preston and A. Gamer, MTMS September 2003

Activity: The Function Machine

A function machine takes an input number x, performs some operations on that number and produces a new output number y. Below are some function machines, showing the input x, and the output y. Can you figureout what the machine did to the input?

In problems 9 and 10

a. Create your own function machine by starting with a rule.

b. Give at least three inputs and the corresponding outputs.

c. What does the graph of your rule look like?

9.

10.

To check your work on your calculator:

1. Press ! and clear out any equations by pressing C and turn off any plots by highlighting them and pressing e. /
2. In Y1= enter the rule x+2. /
3. To view the table of inputs and outputs press `ê /
4. Use the arrow keys to scroll the x values and verify the y values. /
5. To see a graph of the function rule first set up the viewing window by pressing @ and entering the numbers as in the diagram. This sets up the “graph paper”. /
6. To view the graph press % /
7. Pressing $ and the arrow right and left will give you other inputs and outputs that satisfy the rule. /
8. To test other rules press !. You can then C out the current rule, and enter the rules one at a time or all at once in Y1 to Y8. You can then press `ê to see the TABLE(S) or % to view the GRAPH(S). /


Hit The Target

Activity Overview

In this activity, you will use the TI-84 Plus C Silver Edition graphing calculator or TI-SmartView™ Software to write an equation (or equations) that passes through the target point(s).When writing the equations of functions, you will also use split screens with graphs, lists, and tables.

Step 1:
Press! and clear out any equations. /
Step 2:
PressSthen 1:Edit and clear out any data in L1 and L2. /
Step 3:
Enter target point by entering the x-coordinate in L1 and the y-coordinate in L2. The target point entered here is (3,2). /
Step 4:
Press ` ! eto turn on StatPlot1 and configure. /
Step 5:
Use`éto configure the graph screen. /
Step 6:
PressMand select GRAPH-TABLE. /
Step 7:
Press@and configure this ‘friendly’ window. /
Step 8:
Press%.
Step 9:
Now the challenge... Press!and enter a linear equation which passes through the target point:
  • With a positive slope.
  • With a negative slope.
  • With a zero slope.
Once you have successfully completed this task, PressSthen 1:Edit and change your target point or add some other points to the list; Clear out the Y= equations and press%. /

MIX and MATCH

MIX and MATCH highlights multiple representations of linear equations and is an excellent review activity and/or alternative assessment. It is best used in a cooperative group setting.

Materials:

  1. Instructions – page 1
  2. Mix and Match Activity Sheet - page 2
  3. Graphs, descriptions, equations, tables – pages 3 and 4
  4. Envelopes
  5. Glue sticks

Instructions:

  1. On pages three and four of this hand out there are six graphs, six tables, six equations and six descriptions. Cut out a complete set for each group, mix them up and place them in an envelope.
  1. Form groups of four giving each student a mix and match activity sheet (page 2) and each group an envelope with the mixed up pieces.
  1. The groups will match the graphs, their descriptions, their tables and their equations.
  1. Each member of the group will pick a complete set and paste on their Mix and Match Activity Sheet (page 2) and answer the remaining questions.

MIX AND MATCH Activity Sheet Name______

2. Equation

1. Graph

4. Table

3. Description

Slope=

x intercept =

y intercept =

Write the equation of the line though (4,1) and perpendicular to the equation of the line given in box 2. Also sketch this perpendicular line in box 1.

Which part of the matching activity was the most difficult? Explain why.

Write a real world situation that this graph models.

/ A line which is increasing and has a root of 3.
/ A line with a negative average rate of change and an x intercept of -3.
/ A line which is decreasing with a positive x intercept.
/ A line with a positive average rate of change and a negative root.
/ A line which is neither increasing nor decreasing and with an average rate of change of zero.
/ A line which is not a function
2x - 3y - 6 = 0 / x / -3 / 3
y / -4 / 0
2x + 3y = -6 / x / y
-3 / 0
0 / -2
y = (-2/3)x + 2 / x / -3 / 6
y / 4 / -2
2x - 3y = -6 / x / y
6 / 6
0 / 2
y = 2 / x / 7 / -4
y / 2 / 2
x = 3 / x / y
3 / -6
3 / 2