Section 1

Chapter 2Section 1

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

Is a polynomial function of degree n and a leading coefficient of an.

Example:f(x) =7x5 + 3x4 – 8x3 – x2 + 5x – 4

All exponents are integers greater than or equal to zero.

Polynomial Functions

Name Form Degree

Zero Function Undefined

Constant Function 0

Linear Function 1

Quadratic Function 2


Which of the following are polynomial functions?For those that are, state the degree and leading coefficient.A) B) C) D)


A linear function is a polynomial function of degree 1.It has the form of , where a and b are constants and a ≠ 0.

Vertical lines are not graphs of functions.Horizontal lines are graphs are functions but they are a constant function.

Linear Functions

Given

Finding an Equation of a Linear Functions

Given

A functions 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. Called just rate of change or slope of a line.

Average Rate of Change

Daegu Apartments bought a W50,000,000 building and for tax purposes are depreciating it W2,000,000 per year over a 25 year period using straight line depreciation.1. What is the rate of change of the value of the

building?2. Write an equation for the value of of the building as a

linear function of the time t since the building was placed in service.

3. Evaluate and .4. Solve = 39,000,000

Average Rate of Change

A quadratic function is a polynomial function of degree 2. It has the form of x2, where a is a constant and a ≠ 0. Standard form of a quadratic is Vertex form of a quadratic is , where is the

vertex and is the axis of symmetry.

Quadratic Functions

Finding the vertex when in standard form:Vertex (h, k)

Quadratic Function

Rewrite standard form to vertex form

Quadratic Function

Technology

Section 1