Lumen🪙 0

Functions

📖 Learn🎬 Guided Practice✏️ Practice

Graphs

Functions

A function is a rule linking two quantities. Exchange rates are functions: however many dollars you hand over, one rule tells you the rupees you get back.

Forwards with the rule · backwards with the inverse× 21236510inputoutputto find an INPUT, use the inverse: ÷ 2inverse of add is subtract · inverse of multiply is divide
Output 10? Then the input was 10 ÷ 2 = 5.

A rule linking two variables

A FUNCTION is a relationship between two quantities. Whatever you put in, the rule tells you what comes out. You can exchange 1 Hong Kong dollar for 9 Indian rupees. So for HK$20 you get 20 × 9 = 180 rupees. The rule is 'multiply by 9', and it works for any amount.

Writing it with letters

Choose a letter for each quantity, then write the rule as an equation. Let d be the Hong Kong dollars and r the Indian rupees: r = 9d That single line replaces a whole table. Put any value of d in and it gives you r.

Reading a function back into words

You also need to go the other way — given an equation, say what it means. y = 70x, where x is US dollars and y is Indian rupees, means: 'You can exchange 1 US dollar for 70 Indian rupees.' The number in front of x is the rate: how much y you get for ONE x.

Functions with more than a multiplication

Not every function is just a rate. Angelo is twice as old as Sabrina. If Sabrina is s, then Angelo is a = 2s. But if Angelo were 3 years older instead, it would be a = s + 3. Read the words carefully: 'twice as old' means multiply, 'older than' means add.

Worked examples

HK$20 into rupees

  1. 1 Hong Kong dollar buys 9 rupees.
  2. So 20 dollars buys 20 × 9.

Answer: 180 Indian rupees

Writing the function

  1. Let d be the dollars and r the rupees.
  2. Each dollar gives 9 rupees, so multiply d by 9.

Answer: r = 9d

Reading y = 70x in words

  1. x is US dollars and y is Indian rupees.
  2. The 70 tells you how many rupees ONE dollar buys.

Answer: You can exchange US$1 for 70 rupees

Angelo and Sabrina

  1. Angelo is twice as old as Sabrina.
  2. If Sabrina is s, double it.

Answer: a = 2s

Using y = 1.5x

  1. x is US dollars, y is Libyan dinars.
  2. For US$570, substitute x = 570.
  3. 1.5 × 570 = 855.

Answer: US$570 is 855 dinars

Where you see this in real life

  • Every currency exchange board is a set of functions — one rule per currency.
  • A taxi fare of £2 per mile is the function c = 2m.

Key words

Function
a rule linking two quantities
Variable
a quantity that can change, shown by a letter
Equation
a statement that two expressions are equal
Rate
how much of one quantity you get for one of another
Substitute
replace a letter with its number value
🎬 Try Guided Practice →Skip to Practice →