A LGEBRA Day 1 Polynomial Functions

R ECALL

L EADING COEFFICIENT

E XAMPLE 1

R EAL WORLD – E XAMPLE 2 RESPIRATION The volume of air in the lungs during a 5-second respiratory cycle can be modeled by v ( t ) = –0.037 t t t, where v is the volume in liters and t is the time in seconds. This model is an example of a polynomial function. Find the volume of air in the lungs 1.5 seconds into the respiratory cycle.

E XAMPLE 3

Y OU TRY Find g (2 x + 1) – 2 g ( x ) if g ( b ) = b A.1 B.2 x x – 2 C.2 x x + 10 D.2 x 2 – 2

E XIT S LIP

A LGEBRA Day 2 Polynomial Functions

Zeros of Even- and Odd-Degree Functions Odd-degree functions will always have an odd number of real zeros. Even-degree functions will always have an even number of real zeros or no zeros at all. The number of turns is always one less than the degree.

E XAMPLE 1 For each graph, Describe the end behavior Determine whether it represents an odd-degree or an even-degree polynomial function State the number of real zeros a)b)

Y OU TRY For the graph, determine whether it represents an odd-degree or an even-degree function, and state the number of real zeros.

E XIT S LIP For the graph, Describe the end behavior Determine whether it represents an odd-degree or an even-degree polynomial function State the number of real zeros