9514 1404 393
Explanation:
A function is a relation that maps a given input to one output. The relation can be expressed as a set of ordered pairs: (input, output). Those ordered pairs can be presented as a set, a table, a graph, or an equation.
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Finding the value of a function means determining the output for a given input. When the function is specified by a table, the output value is read from the table at the point where the input value matches the desired input.
In the table in the first attachment, the value of the function for an input of 5 is found in the "output" column on the row where the "input" is 5. That function value is 55.
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A function can also be specified by a graph. The input is the found on the horizontal axis of the graph, and the output value is found on the vertical axis. The graph itself is the locus of all points giving the output for a given input. The value of the function is found by locating the desired input value on the horizontal axis, and finding the vertical coordinate of the point on the graph that is on that same vertical line. For the graph at the second attachment, an input value of 6 corresponds to an output value of 120.
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When the function is specified by an equation, the input value replaces the independent variable in the equation, and the result is simplified. A numerical input often (but not always) results in a numerical output. A literal input may result in a literal expression as the function's output value.
For example, consider the function ...
f(x) = 3x +2
An input of x=2 will be found to give an output of ...
f(2) = 3(2) +2 = 8 . . . . 8 is the function value
An input of 2b will give an output of ...
f(2b) = 3(2b) +2 = 6b +2 . . . . a literal expression is the function value
