UNIT FIVE: POLYNOMIAL FUNCTIONS
Lesson One: Introduction & Review
Definitions:
1. Polynomial Expression: See definition on p. 81. Main point is that the exponents are
positive whole numbers.
y  3x  4
Examples:
2x 2  y  9
y  3x 4  5 x  2 x 3
ARE polynomial expressions.
xy 2  2 x 4 y 3  4  0
y  x2  x 1
y  x 3  9
1
y 2
x
y  sin 2 x
These are NOT:
y  2 x 1
2. Relation: A relationship between two variables that may be expressed as an equation
y  2x  1 , a table of values
A graph:
Or a mapping diagram:
-1
4
2
7
6
1
,
X
Y
-2
5
-1
7
0
9
1
11
2
13
3.
Function: A relation in which for every x-value, there is one AND ONLY ONE y-value.
Example:
y  x 2 IS a function
x  y 2 IS NOT a function
Why? Because in the second relation there are TWO possible y-values.
i.e., if y=-2, x=4 and if y=2, x=4 also.
4.
5.
Vertical Line Test for a Function: If a vertical line passes through the graph of a relation
more than once, the relation IS NOT a function. Otherwise, it is a function
Domain: The set of all x-coordinates in a relation.
6. Range: The set of all y-coordinates in a relation.
7. Degree of a term: The sum of the exponents on the variable(s).
Example: The degree of
5 x 5 y 2 is 7.
Example: The degree of
4 2 x 4 y 6 is 10.
8. Degree of a Polynomial: The degree of the highest term.
Example: The degree of
2 x 2 y 3  xy6  5 y 8 is _______________________.
9. Leading Coefficient: The number in front of the term with the highest degree. The
leading coefficient of 3 x  6 x  7 x  2 is ________________________.
5
2
10. Constant Term: The term without a variable. The number that is by itself.
The constant term of 3 x  6 x  7 x  2 is __________________________.
5
2
More Examples: Determine whether the following are functions. Justify your answer.
a)
X
1
2
2
3
4
5
y
5
6
7
8
9
10
b)
c)
2
4
6
8
10
12
14
16
1
3
5
7
9
11
13
15
Some standard graphs and their names:
1. Linear
2. Quadratic
3. Cubic
4. Reciprocal
5. Circle
6. Exponential
7. Sinusoidal
Write underneath each one if it is a function or not a function.
Hw P. 82-84 #1-4,6-8,9,11ab