Date: ______
Algebra III/Trig
3.2 Polynomial Functions of Higher Degree
Goal:
Graphs of Polynomial Functions:
1. Continuous Functions:
2. Simplest Monomial Functions:
if n is even:
The Leading Coefficient Test:
if n is even and the leading
coefficient is positive:
if n is odd and the leading
coefficient is positive:
if n is odd:
if n is even and the leading
coefficient is negative:
if n is odd and the leading
coefficient is negative:
Date: ______
Examples of the Leading Coefficient Test: For the following problems, determine the right and
left-hand behavior of the graph of the polynomial function.
1. f(x) =
x3 + 4x
3.
2. f(x) = 2x2 – 3x +1
4. g(x) = -x3 + 3x2
Real Zeros of Polynomial Functions:
For a polynomial of degree n, the following are true:
1.
2.
When f is a polynomial function and a is a real, the following statements are equivalent:
1.
2.
3.
4.
Finding real zeros:
Step 1:
Step 2:
Step 3:
Date: ______
Examples of Finding Real Zeros: Find all real zeros of the following functions. Then determine
the maximum possible number of turning points of the graph of the function.
1. f(x) = x4 –x3 – 30x2
2. f(x) = ⅓ x2 + ⅓ x – ⅔
3. g(x) = 5x3-10x2-5x
4. h(t) = t2 – 6t + 9
Repeated Zeros / Multiplicity:
1. When k is odd:
2. When k is even:
Graphing Polynomial Functions By Hand: Sketch the function f(x)= x3 – 25x
Step 1:
Step 2:
Step 3:
Step 4: