Math 106 class notes and HW

The HW is Sec 5.2 pp 291-292, #25-40.

I'll pass the tests back tomorrow and set up appts with those who need them. 

NOTES

1. Reviewed notation of polynomial (sum of monomial terms).

2. The degree of a polynomial is the highest power of the variable.

3. The notations f(x), g(x) P(x) and so on are simply the "functional notation" for y.

4. By "domain of a function" we mean the set of all x that "make sense" for that function.

5. y = P(x) can be solved for any value of x in the reals, since the "domain" of any polynomial is the

set of all the real numbers "R" since P(real number) is defined for all polynomials. For example, y=

P(x) = 3x - 7 is defined for any x in R. (Try it: P(-13) = 3(-13) - 7 = -46, for example.)

6. The shapes of the y = x^2 and x^3 type polynomials: the x^2 type are parabolas; the x^3 are cubics

(like a snake).

5. Finding the y-intercept of a polynomial is always easy:  just substitute x = 0 into the equation and

find  y. Function notation is f(0) = y.

6.  The x-intercepts are called the 'roots' of the polynomial. They are also called the 'zeroes'. 

7. Finding the roots requires us to factor the polynomial. Factoring is the next big idea.

8. Although we can factor high degree polynomials, we will be graphing only parabolas for a while.