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Functions and their properties
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The concept of a function as a mathematical machine, the notation f(x)=…, and function tables / diagrams.
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Function as a mathematical machine
SL Core 2.2
A function is like a mathematical machine, you put in a number and it gives you exactly one number back. If you put in the same number multiple times, you will always get the same number out.
An example of a function is the rule "double the input and add 1".
If you input 3, it doubles to make 6, thenwe add1toget an output of7
If you input −5, it doubles to make −10, thenwe add1toget an output of−9
Expression of a function f(x)
SL Core 2.2
The rule that defines a function is often written in the form
f(x)=somethingthatdependsonx
For example, the function "double the input and add 1" can be written
f(x)=2x+1
Let's break down what this expression says:
The LHS names the function f, and then f(x) means "when you input x into the function f"
The RHS defines the rule, and essentially says "the output is twice the input, plus 1".
Evaluating functions
SL Core 2.2
A function can be evaluated for specific values of x by plugging the value into the expression of the function.
Function diagram
2. Prior learning
A function diagram shows how a set of inputs is mapped to a set of outputs with arrows pointing from inputs to outputs.
Multiple arrows can point to the same output, but each input must have exactly one arrow, since a function always gives the same output for a given input.
Table of function values
2. Prior learning
The inputs and outputs of a function can be represented in a table where one row shows inputs, and the other shows outputs:
To find f(some value), look for that value in the first row, then look at the row below it. For example, f(11)=2.
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