1. Polynomial Functions of Higher Degree
Sec. 3.2
Polynomial Functions of Higher Degree

2. Graphs of Polynomials
The graph of a polynomial is continuous (no breaks) p.270
And has only smooth rounded turns (no points like abs. value) p. 270

3. The simplest is a monomial
f(x) = xn n is an integer > 0

4. Ends of the graph
If n is even the ends of the graph go the same direction
If n is odd the ends of the graph go different directions
The greater n the flatter the graph at the origin P. 271

5. Ex. What would the ends of the following look like?
f(x) = -x3 + 2x2 – 1
f(x) = 3x6 +2x2 …

6. Zeros of Polynomial Functions
Zero – same as x-intercepts or solution
Has at most n zeros (n is the degree)
Has at most n-1 turning points

7. Find zeros by factoring
Ex. 4
f(x) = x3 – x2 -2x
Ex. 5
f(x) = -2x4 + 2x2

8. If the degree of the factor is even, the graph touches the x-axis but does not cross.
If the degree of the factor is odd, the graph crosses the x-axis

9. Examples
f(x) = -x5 + 6x3 -9x
f(x) = 3x4 +3x3 – 90x2

10. Intermediate Value Theorem
Let a and b be real numbers such that a < b. If f is a polynomial function such that f(a) ≠ f(b), then, in the interval [a,b], f takes on every value between f(a) and f(b).
Tells you there is no break (gap) between two x-values if it is a graph of a polynomial.

11. Homework
P , odd, even, odd