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independent variable, or argument of f , whereas y is often called the dependent variable.
As we shall see, the process of a function f is usually described using an algebraic formula. For
example, suppose a function f takes a real number and performs the following two steps, in sequence
1. multiply by 3
2. add 4
If we choose 5 as our input, in step 1 we multiply by 3 to get (5)(3) = 15. In step 2, we add 4 to
our result from step 1 which yields 15 + 4 = 19. Using function notation, we would write f (5) = 19
to indicate that the result of applying the process f to the input 5 gives the output 19. In general,
if we use x for the input, applying step 1 produces 3x. Following with step 2 produces 3x + 4 as
our ﬁnal output. Hence for an input x, we get the output f (x) = 3x + 4. Notice that to check our
formula for the case x = 5, we replace the occurrence of x in the formula for f (x) with 5 to get
f (5) = 3(5) + 4 = 15 + 4 = 19, as required. 1.5 Function Notation 45 Example 1.5.1. Suppose a function g is described by applying th...

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