What is a function?
- A function is simply a mathematical “machine” that takes one set of numbers and changes them into another set of numbers according to a set rule
eg. If the function (rule) is “double the number and add 1”
- Putting 3 in to the function would give 2 × 3 + 1 = 7 out
- Putting -4 in would give 2 × (-4) + 1 = -7 out
- Putting a in would give 2a + 1 out
- The number being put into the function is often called the input
- The number coming out of the function is often called the output
What does a function look like?
- A function f can be written as:
f(x) = … or f : x ↦ …
which mean exactly the same thing
- eg. The function with the rule “triple the number and subtract 4” would be written:
f(x) = 3x – 4 or f:x ↦ 3x – 4
- In such cases, x would be the input and f would be the output
- Sometimes functions don’t have names like f and can be written as y = …
eg. y = 3x – 4
How does a function work?
- A function has an INPUT (x) and OUTPUT (f or y)
- Whatever goes in the bracket (instead of x)with f, replaces the x on the other side
eg. For the function f(x) = 2x + 1
- f(3) = 2 × 3 + 1=7
- f(-4) = 2 × (-4) + 1 = -7
- f(a) = 2a + 1