From the rule to the points and the table

Change the coefficients in f(x) = ax + b. Choose an entry and check the highlighted line in the table. The domain of this activity is ℤ; the window only shows entries from −4 to 4.

Em telas pequenas, deslize o gráfico na horizontal para ler os detalhes.

Each point associates an entire input with an output. Vertical scale adjusts; read the values.

A second standard: Pascal

Select line 4. How do your values ​​emerge? Compare the sum of the row with 2⁴.

Em telas pequenas, deslize o gráfico na horizontal para ler os detalhes.

The first line is the zero line. Internal values ​​add the two neighbors immediately above.

Your mission: connect arithmetic and algebra

Review the Fundamental II track when you need to. Start with Pascal’s triangle, then explore the functions chapter. It brings together discovery of functions, Cartesian plane, classification and graphs.

Integers can represent inputs to a function. Your result depends on the rule: an entire entry does not guarantee a complete output. For f(x) = x/2, for example, f(3) = 1,5.

Whole Inputs Laboratory

For f(x) = 2x − 1, calculate the outputs when x is −2, −1, 0, 1, and 2. Mark the points on a Cartesian plane. If the domain is just ℤ, should we fill in the spaces between them?

Check out the investigation

The outputs are −5, −3, −1, 1 and 3. The points are (−2, −5), (−1, −3), (0, −1), (1, 1), and (2, 3). With domain ℤ, we draw separate points: intermediate positions do not belong to the domain.

To conclude: create a function that transforms integers into integers and another that can produce fractional results.