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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