AP Precalculus - Topic 1.4 & 1.5

Degree

Largest exponent

Leading coefficient

coefficient of the variable with highest degree

Relative (Local) Extrema

A polynomial has a relative min or max where the function changes from increasing to decreasing or vice versa

Absolute (Global) Extrema

The greatest relative max (absolute max) and the lowest relative min (absolute min); includes other relative extremas; infinity and negative infinity are not considered an absolute max or min; if domain is restricted, endpoints are considered absolute extremas

What is the polynomial end behavior for a positive leading coefficient and even degree?

Ends of graph both go up

What is the polynomial end behavior of a negative leading coefficient and even degree?

Ends of graph both go down

What is the polynomial end behavior of a positive leading coefficient and an odd degree?

Left end goes down and right end goes up

What is the polynomial end behavior of a negative leading coefficient and an odd degree?

Left end goes up and right end goes down

What is the domain for all polynomials?

All real numbers

What is the range for odd degree polynomials?

All real numbers

What is the range for even degree polynomials?

The range is restricted; a calculator is needed to find the “floor” or “ceiling” of the function

How do you find the x-intercepts of a polynomial?

x-intercepts = degree (n)

How do you find the max # of relative extremas of a polynomial?

One less than degree (n-1)

How do you find the # of points of inflection of a polynomial?

Two less than degree (n-2)

How do you find the y-intercepts of a polynomial?

Always one (all functions have one y-intercept); f(0) = constant