3. Polynomial Functions
A polynomial function has to have
exponents that are whole numbers
The following are NOT polynomials:
3 2
y 2x 4 x 5x
3
y 3
x
x
y 8
4. Degree and Name
Degree – highest exponent of a
polynomial
Constant
Linear
Quadratic
Cubic
Quartic
Quintic
5. Homework Answers – p106
10. a. r = ks
b. 1.1; r = 1.1s
c. about 45 mi/h
11. b. F(v) = (60/9)v2 or F(v) = 6.67v2
c. 540 N
14. No, there is an exponent that is a variable, not a constant
16. a. d = 1, linear function or polynomial function of degree 1
b. f(6) = 2; f(0) = -7
c. -10
18. d = 3; f(2) = -1
6. Direct Variation Functions
A function that has no translation (shift)
and has some symmetry
Exs.
y = 2x
y = -4x2
y = 3x3
y = -1/2x4
8. Graphing from Factored Form
Find the following:
1. zeros (from the factors) and plot them
2. y-intercept (let x = 0)
3. degree to get the end behavior
4. x-values in between zeros to get a
sketch of the graph
9. Graph y = 3x3 – 12x
First, factor the polynomial.
Show x and y intercepts!
10. Multiplicity
A multiple zero is a repeated zero.
Multiplicity is the number of times the
related linear factor is repeated in the
factored form of a polynomial.
– use the exponent of the factor to determine it.
2 3
y ( x 2) ( x 2) ( x 5)
11. Standard form terms are written in descending
order and all “like terms” are combined
12. Writing a polynomial in standard
form.
Example:
y = (x – 1)(x + 2)(x – 4)
What is the degree of the function?