Functions and Function Notation

Concept

Function Notation

Function notation is a special way to write functions that explicitly shows that y is a function of x — in other words, that y depends on x. Function notation is symbolically expressed as y=f(x) and read y equals f of x. Equations that are functions can be written using function notation. ccc Equation & & Function Notation [1ex] y=-5x+4 & & f(x) = -5x+4 Notice that y has been replaced by f(x). In function notation, x represents an element of the domain and f(x) represents the element of the range that corresponds to x. When written in function notation, the expression that describes how to convert an input into an output — the right-hand side expression — is called the function rule.

Besides f, other letters such as g or h can be used to name the function. Similarly, letters other than x can name the independent variable.

Extra

Interpreting Function Notation
To interpret an equation given in function notation, it is necessary to understand what both sides of f(x)=k mean. For example, consider the following equation. f( 3) = 12 Here, f( 3) denotes that the function's input is x= 3 and that 12 is the output corresponding to this input. f( 3) = 12 ⇓ The output offwhenx= 3 is 12. Now, consider a different scenario. Let w(t)=200t be a function that describes the number of words Kevin reads in t minutes. The following statements are true for this function. w(4) and w(t)=900 Here, w(4) is the number of words that Kevin reads in 4 minutes and can be found by evaluating the function for t=4. However, the input is not a particular number in the second statement. In such cases, the statement can be interpreted as a question. w(t)=900 ⇓ For which value oft is the output equal to900? Based on the context, the second statement asks how many minutes it takes Kevin to read 900 words. To find this value of t, the equation w(t)=900 has to be solved for t.

Exercises
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