AP precalculus 1.1-1.6

What is a function

a relation that assigns exactly one output for every input from its domain. It is often represented as f(x), where x is the input variable.

What is the domain

the set of input values of a function and is represented by the independent variable

What is the range

the set of output values of a function that is represented by the dependent variable

What are the zeros of a function

the input values (x-values) for which the output (f(x)) equals zero. They represent the points where the graph of the function intersects the x-axis.

rate of change formula

Y₁-Y₂/X₁-X₂

Describe the graph of k

Graph of k is decreasing and the AROC is negative. The graph of k is concave down and the average rate of change is decreasing. The graph of k is decreasing at t decreasing rate

Describe the graph of h

Graph of h is decreasing and the AROC is negative. Graph of h is concave up and the AROC is increasing. The graph of h is decreasing at an increasing

Describe the graph of g

Graph of g is increasing and the AROC is positive. graph of g is concave down and the AROC is decreasing. the graph g is decreasing at a decreasing rate

describe graph of f

Graph of f is increasing and the AROC is positive. the Graph of f is concave up and the AROC is increasing. Graph of f is increasing at an increasing rate.

How do you know if a function is linear

because the AROC is constant

How do you know if a function is Quadratic

because the AROC of the AROC is constant

What are the rules of a polynomial

a_{n}x^{n}+a_{n-1}x^{n-1}\ldots 

Where 

• n is a positive integer

• a is a real number and a_n is not equal to zero

• the polynomial’s degree is n

• the polynomial  leading coefficient is a_n

What is the multiplicity

how many times a zero occurs

if a degree is even what is the end behavior like

they go the same way

if a degree is odd what is the end behavior like?

they go different ways

how do you know if a polynomial has absolute max or min

if the degree is even it does. If odd it does not

if the degree is even and the leading coefficient is positive what does it mean 

there is an absolute min

if the degree is even and the leading coefficient is negative what does it mean 

there is an absolute max

what is a relative or local maximum

the highest point on the graph in a small region

what is relative or local min

the lowest point on the graph in a small region

what is the absolute or global max

the highest point of the graph

what is the absolute or global min

the lowest point of the graph

how can you tell how many zeros a polynomial has

by looking at the degree

if the multiplicity is even what does that mean

it ‘bounces’ off the x axis

if the multiplicity of a polynomial is odd what does that mean

it ‘cuts’ through the x axis

how to prove a polynomial is even analytically

ensure that f(-x)=f(x)

how to prove a polynomial is odd analytically

ensure that f(-x)=-f(x)