Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
3. Function Notation
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Exercise 1 Page 122

To evaluate a function for a given value of the variable, substitute the value for the variable.

-13, -5, and 1

Practice makes perfect
Evaluating a function for a certain value of x means that we substitute the given value for every instance of x. Let's do this for the given function when x=-4.
f(x)= 2x-5
f( -4)=2( -4)-5
f(-4)=-8-5
f(-4)=-13
When x=-4, the function's value is - 13. We will evaluate this function for x=0 and x=3 in the same way using the table below.
x 2x-5 f(x)
-4 2( -4)-5 -13
0 2( 0)-5 -5
3 2( 3)-5 1

Extra

Functions
Let's recall some information about functions. A function is a relation in which each input is assigned to exactly one output. The set of all possible inputs is called the domain of the function and the set of all possible outputs is called the range. If x represents the inputs and y the outputs of a function, it is often said that y is a function of x or that y depends on x. y = f(x) This way of representing the dependent variable is called function notation. A function can be represented using a table, a mapping diagram, an equation, or a graph.
Representations of functions
Note that every function is a relation, but not every relation is a function. In the following applet, three different relations are analyzed to determine whether they are functions.
Three different mapping diagrams. The second one is not a function because one input has two outputs.
In Relation III, although one of the outputs corresponds to two different inputs, it is still a function because each input has exactly one output. Depending on how a relation is represented, there are different methods to determine whether or not it is a function.
Determining Whether a Relation Is a Function
If represented as Use
A set of coordinates or a table of values A mapping diagram
A graph in the coordinate plane The Vertical Line Test