Today in Pre-Calculus You will get your test back tomorrow. Notes: –Polynomial Functions –Linear Functions Homework.

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Presentation transcript:

Today in Pre-Calculus You will get your test back tomorrow. Notes: –Polynomial Functions –Linear Functions Homework

Polynomial Functions Let n be a nonnegative integer and let a 0, a 1, a 2, …., a n-1, a n be real numbers with a n ≠0. The function given by f(x) = a n x n + a n-1 x n-1 +…+a 2 x 2 + a 1 x + a 0 is a polynomial function of degree n. The leading coefficient is a n. 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 NameForm Degree Zero Functionf(x) = 0 Undefined Constant Functionf(x) = a (a≠0)0 Linear Functionf(x) = ax + b (a≠0)1 Quadratic Function f(x)=ax 2 +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.

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

Modeling Pg 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 = -$2,000t t=5.5 years

Homework Pg. 182: 1-10 all, 52, 56