What is function notation? Sometimes, the domain values (inputs) are related to the range values (outputs) with a rule.
For example, take a look at the following situation.
Input function rule output
2 3 times input + 1 7
3 3 times input + 1 10
You can just use x to represent the inputs and y to represent the outputs and write
y = 3 times x + 1
y = 3x + 1
The notation y = 3x + 1 is one way to write this function. However, there is another way. It is the function notation.
A function is in function notation when you use f(x) to indicate the outputs. You read f(x) as " f of x " or " f is a function of x "
Note that f(x) does not mean " f times x "
Suppose that the value of x is 6. You can write f(6) and f(6) is read " f of 6 " or " f is a function of 6 "
f(6) represents the value of the function at x = 6.
For the example above, you can write f(x) = 3x + 1
f(6) = 3 times 6 + 1 = 18 + 1 = 19
There is nothing wrong with the notation y = 3x + 1. However, it has some limitations.
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