An Introduction to Functions Slideshow 22, Mathematics Mr Richard Sasaki, Room 307

Objectives To learn what a function is and necessary notation To apply functions to sets of numbers Understanding basic rules and restrictions on functions

Functions A function is a process that changes something. We input something, it is processed and then an output is left. Process Input Output 12 48 ×4

𝑓( ) 𝑥 = 2𝑥+4 Notation A function of something is denoted as… 𝑓( ) 𝑥 = 2𝑥+4 For a function of a variable 𝑥, we would write… We can state what we want the function to do here. So this means for a number 𝑥, the function doubles it and then adds 4 to it.

2·4+4 12 𝑓( ) 𝑥 = 2𝑥+4 𝑓( ) 4 = = Specific Values Try the worksheet! Let’s try inserting the value 4. 𝑓( ) 𝑥 = 2𝑥+4 𝑓( ) 4 = 2·4+4 = 12 Basically this is the same as substituting 𝑥=4 into the function.

Answers 26 -10 -9 -8 -7 -6 -5 -4 -10 -5 0 2 8 18 32 50 72 -4 10 8 6 4 2 0 -2 𝑓(𝑥) = 3𝑥 − 4 𝑓(3)=5, 𝑓(4)=8, 𝑓(5)=11,

Rules for Functions A function must work for all numbers it was designed for. But this doesn’t put restrictions on results missing. This is not allowed, an inputted value must have exactly 1 result. It is fine if not every number is included as an answer. We’ll look at this in more detail in later lessons.

What are sets? Sets are the basis of mathematics. They are basically a collection of things. For example, the set of colours in the rainbow is {𝑅𝑒𝑑, 𝑂𝑟𝑎𝑛𝑔𝑒, 𝑌𝑒𝑙𝑙𝑜𝑤, 𝐺𝑟𝑒𝑒𝑛, 𝐵𝑙𝑢𝑒, 𝐼𝑛𝑑𝑖𝑔𝑜, 𝑉𝑖𝑜𝑙𝑒𝑡}. A set is a group of elements (eg: Red) in curly brackets {𝑙𝑖𝑘𝑒 𝑡ℎ𝑖𝑠}. They must be separated by commas. Order has no meaning.

Answers 6 Yes 52 {1, 2, 3, 4, 5, 6} 𝑓(𝑥)=2𝑥 −4 to 11 (or 15) {5, 6, 7} Yes −4 to 11 (or 15) No, 𝑓(4) can only be one value. Yes it is. 5 𝑓(𝑥)=20𝑥 𝑓(𝑥)=2𝑥 𝑓(6)=120𝑐𝑚 Because it is inaccurate. A 20 year old is not 4m tall. Yes Eg: 𝑓(𝑥)=7𝑥+110 52 𝑓(𝑥)=20𝑥 Negative numbers or very high ones Hearts, Diamonds, Clubs, Spades 𝑓(40)=800𝑐𝑚 or 8𝑚 Approx {0, …, 50} Negative numbers cannot be entered (without including imaginary numbers).