# 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 **conjecture** 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

*a*or*b*of the linear function*f*(*x*) and the parameters of*c*or*d*of the linear function,*g*(*x*), 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.