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tomorrow.• Notes:

– Polynomial Functions– Linear Functions

• Homework

Polynomial FunctionsLet n be a nonnegative integer and let a0, a1, a2, …., an-1, an be real numbers with an ≠0. The function given by

f(x) = anxn + an-1xn-1 +…+a2x2 + a1x + a0

is a polynomial function of degree n. The leading coefficient is an.

Simply put: Exponents can’t be negative or fractions, the highest power in the polynomial is the degree of the function, the coefficient of this term is the leading coefficient.

Page 170 Example 1.

Polynomial Functions of No or Low Degree

Name Form Degree

Zero Function f(x) = 0 Undefined

Constant Function f(x) = a (a≠0) 0

Linear Function f(x) = ax + b (a≠0) 1

Quadratic Function f(x)=ax2+bx+c (a≠0) 2

Average Rate of Change

(a.k.a slope)

Theorem: A function defined on all real numbers is a linear function iff it has a constant nonzero average rate of change between any two points on its graph.

( ) ( )change in y f b f a

change in x b a

Examples

1. Find the slope of the line of f such that f(3) = 4 and f(-1) = -8

2. Find the equation of the line of f.

y – 4 = 3(x – 3)

y – 4 = 3x – 9

y = 3x – 5

4 83

3 1

ModelingPg 173: Exploration 1:.

1.What is the rate of change of the value of the building?

2.Write an equation for the value v(t) of the building as a linear function of the time t since the building was placed in service.

3.Evaluate v(0) and v(16)

4.Solve v(t)=39,000

-$2,000

v(t) = -$2,000t + $50,000

$50,000 $18,000

39,000=-$2,000t + $50,000-$11,000 = -$2,000tt=5.5 years

Homework• Pg. 182: 1-10 all, 52, 56