Unformatted text preview: elations and Functions 1.5 Function Notation In Deﬁnition 1.4, we described a function as a special kind of relation − one in which each xcoordinate is matched with only one y -coordinate. In this section, we focus more on the process
by which the x is matched with the y . If we think of the domain of a function as a set of inputs
and the range as a set of outputs, we can think of a function f as a process by which each input
x is matched with only one output y . Since the output is completely determined by the input x
and the process f , we symbolize the output with function notation: ‘f (x)’, read ‘f of x.’ In this
case, the parentheses here do not indicate multiplication, as they do elsewhere in algebra. This
could cause confusion if the context is not clear. In other words, f (x) is the output which results
by applying the process f to the input x. This relationship is typically visualized using a diagram
similar to the one below.
(Inputs) y = f (x)
(Outputs) The value of y is completely dependent on the choice of x. For this reason, x is often called th...
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