Four Ways to Represent a Function

In calculus, there are four ways to represent a function.

• Verbally, by using words.
• Visually by using a graph.
• Algebraically, by using a formula.
• Numerically, by using a table.

However, what is a function?

A function is a rule that assigns to each element x in a set D exactly one element, called f(x), in a set E. 

All this means though, is that a function is a rule that gives us only one value f(x) in a range for every
value of x in a domain.

When we represent a function, we use two different types of marks to signal closed and open points.

• For closed points, we write " [ ] " 
• For open points, we use " ( ) " 

Domain & Range

• Domain: In a graph, from left to right, in a function, we call all values of x the domain of the function.
• Range: From bottom to top, all values of y we call the range of a function.

Increasing & Decreasing Intervals

• The decreasing intervals of a graph are simple to determine just by looking at the graph. 
• When a graph increases, the first value of x will be lower than the second value. Alternatively, a graph that decreases will have  a higher first value than the second.