Home page for accesible maths Math 101 Chapter 2: Functions of a real variable

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2.6 Graphs and Continuity

Graphs

In calculus we consider real functions, and it is helpful to drawn graphs. The domain is drawn horizontally and the codomain is drawn vertically on the usual (x,y)(x,y) Cartesian axes.

The graph consists of the points (x,y)(x,y) such that y=f(x),y=f(x), which gives a special type of curve.

Traditionally xx is called the independent variable and yy the dependent variable.

In Lab100, the software RR will be used to sketch graphs; meanwhile we look at some basic examples to illustrate the terminology.

2.6 Example

The graph of f::f:{\mathbb{R}}\rightarrow{\mathbb{R}}: f(x)=2x2-1f(x)=2x^{2}-1. What is the range of ff?

Solution. The range of ff is [-1,)[-1,\infty).