What f(x) means, working out f(3) and f(−2), writing f(a + 1) as an expression, and solving f(x) = k.
What you will learn
- Work out values such as f(3) and f(−2)
- Write f(a + 1) or f(x + 2) as a simplified expression
- Solve f(x) = k
A function is a rule with a name
f(x) = 3x − 5 is a rule called f.
Whatever goes in the bracket replaces every x in the rule.
- f(4) = 3 × 4 − 5 = 7
- f(−2) = 3 × (−2) − 5 = −6 − 5 = −11
Brackets round a negative input stop sign slips, especially with powers: if g(x) = x² + 1, then g(−3) = (−3)² + 1 = 10, not −8.
A function can also be given in words: "f multiplies a number by 4, then subtracts 7" is f(x) = 4x − 7. "Subtract 7, then multiply by 4" is f(x) = 4(x − 7): the order matters.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- A function is a rule with a name
- An expression in the bracket
- The mistakes to avoid
- Try it: An easy start
8 practice questions, marked as you go; about 20 minutes in all.
Key terms
Every, Output
In this unit: Functions and graph transformations
Function notation, composite and inverse functions, the shapes of standard graphs, translations and reflections of y = f(x), and the graphs of sin, cos and tan (Higher).