1.1 to 1.3 Just the Facts, Ma’am.

A Review of some basic concepts before we get into big deal

Calculus (Oh I can’t wait!!!)

What is a Function?

Definition: The set of (x, y) pairs such that each x has its own unique y value.

The x values of a function are called the Domain of the Function and all the y values are called the Range of the Function.

X is called the “independent variable” while y is the “dependent variable”

DomainThe domain is the set of x values that are

allowed in the function.

The easiest way to define the domain (all the x values possible) is to define what the domain can’t be.

Look for square roots (which must be positive) and fractions (which can’t have zeroes in the denominator. Other than that, pretty much anything goes.

RangeThe range is the set of y values that come out

of the function.

You can determine the range by either looking at the graph, or also looking at what you can put in and what would come out based on the domain.

Example: Find the domain and range of the function

2

1f(x)

x

Odd/Even Functions

“Odd” and “even” are ways of describing symmetric properties of functions.

Odd Function: f(–x) = – f(x)

Even Function: f(–x) = f(x).

Come up with an odd function and an even function and lets look at them graphically.

Is everything Odd or Even? No, it could be neither.

Graph ShiftingGiven f(x)

Graph of f(x+h) Shifts graph left h units

Graph of f(x–h) Shifts graph right h units

Graph of f(x)+k Shifts graph up k units

Graph of f(x)–k Shifts graph down k units

Compositions

f ◦ g f(g(x)) g ◦ f g(f(x))

1

h(x)3x

x 1

g(x)x 5

2f(x) x 3

a) f(x) ◦ g(x) b) g(x) ◦ f(x)

1. If and find

1

g(x)x

2. If , and

find f ◦ g ◦ h.

f(x) 2x 1 2g(x) x

3. If and find f ◦ g

x 6

f(x)x 4