4A. Functions

Functions

You encountered functions when you studied algebra. In general, you use a function in an expression by writing the function name followed by the arguments, in parentheses. The parentheses are required. In algebra, functions typically have names that are a single letter. C++ supports functions, but their names can have any length. Each argument of a function can be any expression. For example, the value of expression sqrt(9.0 + 16.0) is approximately 5.0. If there are two or more arguments, separate them by commas. For example, function pow(x, y) produces xy C++ expression pow(2+3, 4/2) has value 25.0.

Evaluating expressions

Evaluate an expression from the inside out. For example, if f (x) = x + 1, then expression f (3+2) + 1 has value 7, computed as follows. f (3+2) + 1 = f (5) + 1 = 6 + 1 = 7 and f (4) + f (10) = 5 + f (10) = 5 + 11 = 16

Terminology: calling a function

An expression that uses a function is referred to as a function call, and we say that expression sqrt(2.0) calls sqrt.

Nested function calls

The argument of a function can be any expression, including an expression that uses a function. For example, if f (x) = x + 1, then f (f (10)) = f (11) = 12 and if g(x) = 2*x + 4, then g(g(7) + f (2)) = g(18 + f (2)) = g(18 + 3) = g(21) = 46

Arguments/parameters

If E is an expression and f  is a function, then we say that E is the argument of f  in expression f (E). I will use term parameter interchangeably with argument.

Summary

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  double q = sqrt(36.0);

Exercises

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1. Suppose that g(x) = 3x − 2. What is the value of expression g(g(9) + 1)? Answer

2. Suppose that g(x) = 3x − 2. What is the value of expression g(g(9 + 1))? Answer

3. Suppose that g(x) = 3x − 2. What is the value of expression g(g(9)) + 1? Answer