Zeros of linear functions and their product
- Author:
- Erlina Ronda
- Topic:
- Algebra, Functions, Linear Functions
Question: How are the zeros of linear functions and the zeros of their products related?
Write your answer to the question, and then continue with the tasks below.
Verify you answer by answering the following tasks using the applet.
I. COLLECT DATA: Write the algebraic representations of the functions that you generated using the applet and then write their zeros.
Set A. f(x)= g(x)= h(x)= zeros of f: zeros of g: zeros of f x g:
Set B. f(x) = g(x) = h(x) = zeros of f: zeros of g: zeros of f x g:
Set C. f(x) = g(x) = h(x) = zeros of f: zeros of g: zeros of f x g:
II. NOTICE SIMILARITIES, DIFFERENCES, RELATIONSHIPS
What is the same and what is different in Sets A, B, and C?
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. LOOK BACK
What is your answer to the problem posed at the beginning of this activity?
VI. EXTEND (1)
Is it possible for the product of two linear functions to only have one zero? Why do you think so?
Generate examples of pairs of linear functions where the zeros of the product are additive inverses.
VII. EXTEND (2)
Can the product of any two linear functions be considered a function? Why do you think so?