Graphing Calculator Activity

What’s my Function?

Connie Stoner

Illinois STATE GOAL 8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

STANDARD 8B

Interpret and describe numerical relationships using tables, graphs and symbols.

8.8.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph.

This activity is designed to help junior high students understand how to identify whether equations are linear or not.

Objectives:

  • Students will graph equations on a coordinate plane using graphing calculators.
  • Students will evaluate which equations are linear when graphed.
  • Students will analyze which attributes in the equations make them linear.
  • Students will develop a “rule” for finding when equations are linear and when they are not linear.

Name ______Class ______Date ______

What’s My Function?

Turn on your calculator. The row indicated with the arrow is where the buttons we will be using to explore different function or two-variable equation graphs are.

Press the y= key. Notice that each equation already has y= on the screen. You will need to clear any equations that are already on the screen, and you will need to make sure that the plots are not highlighted.

Press on the zoom key and choose 6. Push enter. Type in each of the following equations, one at a time, press the zoom key and choose 6, Press enter, and then press the graph button.

For each equation, decide if the graph is linear (a straight line) or not. Draw a picture of each graph. Clear the equation before you start the next one.

Equation / Linear? Yes or No / Drawing of Graph
Equation / Linear? Yes or No / Drawing of Graph

(Use the math button. Under “num” you will find abs( which will allow you to enter the absolute value.)

1. Look at the equations that made a linear graph. What do you notice about them? You should have several observations.

2. Look at where the lines cross the y axis. Can you find those numbers in the equation? If so, where are they?

On the linear graphs, what happens when the number in front of the x changes?

3. If the number in front of the x gets bigger, what happens to the line?

4. If the number in front of the x is less than 1, what happens to the line?

5. If the number in front of the x is negative, what happens to the line?

6. If the number is divided by x instead of multiplied, how does that change the graph of the equation?

7. Why does absolute value change a graph so it is no longer linear?

On the netbook, go to the Internet site:

Log in as a student. Student user name: with9summer

Under mathematics choose Introductory Algebra, then coordinate geometry, then math interactive tools

Choose: Grapher: Quadratic Functions

Explore what happens to the graph when you make a = 0, c = 0, and try different numbers for b. What did you discover?

Explore what happens to the graph when you make a = 0, b = 1, and try different numbers for c. What did you discover?

How does the graph change when a = (a number other than 0)?

Explain how you could tell if an equation is linear.