Activity 1. Zeros of linear functions and their product

PROBLEM: How are the zeros of linear functions and the zeros of their products related?

Write your answer or [b]conjecture[/b] here about the relationship between the zeros of linear functions and their products.

TEST CONJECTURE

You can test or verify your conjecture using the following applet. The applet generates linear functions and their products by changing the parameters [i]a[/i] or [i]b[/i] of the linear function [i]f[/i]([i]x[/i]) and the parameters of [i]c[/i] or [i]d[/i] of the linear function, [i]g[/i]([i]x[/i]), using the SLIDER tool.

I. COLLECT DATA: Write the functions that you generated using the applet and then write their zeros.

II. NOTICE SIMILARITIES and DIFFERENCES

What is different and what is same in the entries under Sets A, B, and C? Write as many that you noticed.

III. MAKE CONJECTURES

What statement(s) can you make about the zeros of two linear functions and the zeros of their product?

IV. JUSTIFY CONJECTURES

Can you explain why you think your conjectures will hold even for other pairs of linear functions?

V. REFLECT

What is your answer to the problem posed at the beginning of this activity? In what way is it the same or different?

VI. EXTEND (1)

Is it possible for the product of two linear functions to only have one zero? Why do you think so?

VII. EXTEND (2)

Write a problem that you can investigate further using the GeoGebra app.