The first several problems are “What’s my Rule?” activities. Input values are entered, one at a time, into cell A1 of the spreadsheet. The nomograph displays the input and its corresponding output. By repeatedly entering different inputs, the student should be able to discover the function’s rule.

For example, if domain values 1, 2, 5, and 7 and their respective range values 3, 5, 11, and 15 are observed, the rule f(x) = 2x + 1 should be identified. When students have conjectured a rule, they should record it on their worksheets and check it. The rule is checked by selecting an input number, applying the rule, and predicting the output number.

This nomograph follows a quadratic rule. Students are guided through the same steps to determine the rule. Encourage students to record several of the ordered pairs they observed on their worksheets. This will help them in determining the function’s rule.

Instruct students to create their own functions of the form y = ax + b or y = ax2 + b (where a and b are integers). Each student should use the Calculator work area on page 3.1 and redefine f1 to their own function by using the Recall Function Definition command. Students should then proceed to page 3.2 (to display the nomograph) and exchange handhelds with a partner. It is the partner’s task to use the nomograph to identify the mystery function. Encourage students to repeat this activity several times.

The nomograph on page 4.1 displays a function with restricted domain: f(x)= square root of (x^2-4) . It is also a continuous nomograph—the inputs are changed by grabbing and dragging the point on the domain. As the point is dragged through x-values not in the domain, the function arrow disappears. Students are asked to explain when and why this happens for this specific function. To avoid confusion, make sure the arrow is visible when students first open the file (that is, |x| > 2).