CHAPTER 2Sections 2 and 3

Power Functions and VariationAny function that can be written in the form

is a power function. The constant a is the power, and k is the constant of variation, or constant of proportion.

We say f(x) varies as the ath power of x, or f(x) is proportional to the ath power of x.

Common formulas power functions.

Formula Power Constant of Variation

C 1

2

-2 k

Analyzing Power Functions

State the power and constant of variation for the function, graph it and analyze it.

, rewrite

, rewrite

Monomial Function

Any function that can be written as

where k is a constant and n is a positive integer, is a monomial function.

Two groups, even and odd powers.

Observe the graphs of

Observe the graphs of

End BehaviorGiven

If n is odd, the graph will have opposite behavior.

If n is even, the graph will have the same behavior.

If k is positive, the graph rises to the right.

If k is negative, the graphs falls to the right.

Even or Odd Function

An even function is symmetrical with respect to the y-axis.

An odd function is symmetrical with respect to the origin, it is a 1800 rotational symmetry.

Terminology• Standard Form• Coefficients• Leading Term• Leading Coefficient• Degree of the polynomial

• •

Local Extrema and Zeros of Polynomial Functions Theorem

• A polynomial function of degree n has at most n – 1 local extrema and at most n zeros.

Graphs Facts

Number of turns a graph has:

The graph of a polynomial function of degree n has at most n – 1 turns.

The zeros of the function are the x intercepts of its corresponding graph.