3. Graphs of Multivariable Functions

Graph (2 Dimensional)

Definition

The graph of a function $f$ of one variable with domain $D$ is the set

$(x,y)|x\in D\cap y=f(x)$

In a graph, it has the following:

• Minimum (lowest point on the graph)
• Root (X-intercept)
• Maximum (highest point on the graph)

Graph (3 Dimensional)

Definition

The graph of a function $f$ of two variables with domain $D$ is the set

$(x,y,z)|(x,y)\in D\cap z=f(x,y)$