Category Archives: Message

Week 1: Polynomials – Day 3

1. Make a quick sketch of the function:       f(x) = x2 – 4.

2. Make a quick sketch of the function:       g(x) = (4 – x)2.

3. Let h(x) = f(x)*g(x) = (x2 – 4)( 4 – x)2 . What kind of function is h(x)?

4. How many roots does h(x) have?

5. Make a quick sketch of the graph of h(x). Hint: you can find all the real roots of h(x). Test the values of points between and around the roots; e.g. h(-3), h(0), h(3), h(5).