Labware - MA35 Multivariable Calculus - Single Variable Calculus
 MA35 Labs 1 » Single Variable Calculus Contents1.1 Functions of One Variable 1.1.1 Demo Tutorial 1.1.2 Linear Functions 1.1.3 Domain, Range & Function Graphs 1.1.4 Slices 1.1.6 Continuity 1.4 Integration Search

Domain, Range & Function Graphs

Text

The domain of a function of one variable is a subset of the real line { x | x ∈ {R} }.

The range of a real-valued function f is the collection of all real numbers f(x) where x is in the domain of f.

The graph of a function of one variable is the collection of points (x,f(x)) in the coordinate plane where x is in the domain of f.

Demos

 Domain and Range The function f(x) and its domain are given in the control panel. The graph of f(x) is shown in a separate window. There are two red hotpots that can be moved along the x-axis. These two points are used to specify a green domain, whose image under f(x) is shown in cyan. To view the range of f(x) over the green domain, animate the variable called "ShowRange" in the control panel. This pulls the curve onto the y-axis and, therefore, shows the range of f(x) over the green domain.

Exercises

• 1. What is the range of the function f(x) = ax2? (The answer will depend on the constant a.)
• 2. What is the range of the function f(x) = -x4 + 2x2?