Section A-8: Functions
Expressions in Maple are formulas that are evaluated by using the Context Panel: Evaluate at a Point, or the evaluation template from the Expression palette, or the eval command. Functions in Maple are formulas that are evaluated by using the standard math notation such as fx.
A function is a relationship (or mapping) between two sets. In calculus, the sets are typically sets of real numbers. The formula defining the relationship is called the rule of the function, and is typically an algebraic expression. The sets are called the domain and the range. A function is specified by giving its domain and its rule. Changing the domain changes the function. If a domain for a rule is not explicitly stated, the common convention is to take the domain as the largest set of real numbers for which the rule is defined.
Maple has mechanisms for defining the rule of a function, but does not have a way of attaching a specific domain to a function. Thus, Maple must use the convention that the domain is the largest set of numbers for which the rule is defined. However, there is one exception Maple makes that a calculus text would not make.
For example, Maple will see the rules x2−9x−3 and x+3 as defining equivalent functions since the actual domains differ by just one member, namely, x=3, and the values of the fraction "near" x = 3 are the same values one gets from x+3. Thus, Maple simplifies the fraction to x+3 but a good calculus student would point out that the fraction is not defined at x = 3, so the simplification to x+3 is only valid for x≠3.
Define the function fx=x sinx and obtain the values fπ/4 and f1.3.
Convert the expression x2 cos2 x to a function g, then obtain g2.7.
If hx=1/1+x, obtain the composition hhx. What is the domain of this composition?
Define the piecewise function whose rules are x2+1 for x<2 and x+3 for x≥2.
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