Illuminations: Function Matching

# Function Matching

See how well you understand function expressions by trying to match your function graph to a generated graph. Choose from several function types or select random and let the computer choose.

### Instructions

 Choose Type Choose the type of function you would like to match. Random (Any) will choose among all possible types. Random under each class will only choose a type among that class. Once you start a problem it will be noted with a question mark. Completed problems will be noted with a check mark.   Graph On your graph, you can move the graph by clicking on the empty space and dragging. You can also trace your graph by dragging along the curve. This will show the coordinates of the point you are on. Zoom In/Out changes the zoom of your graph.   Function Expression In the bottom area, enter the values to match the generated graph to your graph. Your function expression is corrected when the graphs match. You can use the arrows to increase and decrease your values or type them in directly with the keyboard. Check checks to see if all your values are correct. Hint reveals one value.   Other Features Reset All resets all function values of all types. It does not give you new problems. Reset resets the function values of the current type. It does not give you a new problem. New gives you a new problem of the current type. Change Type is only active for random types. It allows you to change the type selected for your problem.

### Exploration

 Polynomial Function Matching Choose a second degree polynomial graph. Match a few graphs. Use the Help feature if needed. Can you explain what effect each value has on the graph? Match graphs from all three types. Which values have the same effect regardless of the degree of the polynomial? What are the effects?   Periodic Function Matching Choose a sine graph. Match a few graphs. Use the Help feature if needed. Can you explain what effect each value has on the graph? Why do you think this graph is called periodic? Notice that the function expressions for all the periodic graphs have the same form. Can you explain why?   Any Function Matching Match at least one function of each function type. Use the Help feature if needed. Name common characteristics of all values in all function types. Name dissimilar characteristics of all function types. Can you explain why the function types are grouped the way they are?

### NCTM Resources

 Principles and Standards for School Mathematics (Book and E-Standards CD)

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