Math Analysis

Math Analysis

. Name comes from the fact. that we analyze different  Name comes from the fact that we analyze different mathematical objects

 Most often we analyze functions.

 Sometimes we analyze numbers.

 Sometimes we analyze graphs.

 Sometimes we analyze shapes.

 Sometimes we analyze logical arguments.

We look at how different branches of mathematics are connected.

We look for patterns.

We try to see how math is related to science, music, art, and other fields.

The key idea is … ANALYZE

At other schools this course can be called Precalculus Math IV Functions Mathematical Modeling

Let’s begin by reviewing some basic concepts …

A function is a set of ordered pairs in which each first element is paired with exactly one second element.

A function is a set of ordered pairs in which each first element is paired with exactly one second element.  each x goes with exactly 1 y

A function is a set of ordered pairs in which each first element is paired with exactly one second element.  each x goes with exactly 1 y  each input has only 1 output

A function is a correspondence between two sets A and B in which each element of A corresponds to exactly one element of B.

Domain . Set A . Set of all independent. variables  Domain  Set A  Set of all independent variables  All the allowable input  All the x’s

Range . Set B . Set of all dependent. variables . All the output  Range  Set B  Set of all dependent variables  All the output  All the y’s

In some places in advanced mathematics, range can also be called the codomain.

Functions can be represented as …

Functions can be represented as …  Lists of ordered pairs

Functions can be represented as …  Tables

Functions can be represented as …  Mappings

Functions can be represented as …  Graphs

Functions can be represented as …  Verbal relationships

Functions can be represented as …  Rules (equations)

Functions can be represented as …  Lists of ordered pairs  Tables  Mappings  Graphs  Verbal relationships  Rules (equations)