Worked example 1
Evaluate a function
For f(x) = 2x² − 5x + 1, find f(3).
- Replace x with 3.
- Calculate 2(3)² − 5(3) + 1
- Use powers before multiplication and subtraction.
Answer: f(3) = 18 − 15 + 1 = 4
Higher Mathematics
Higher Maths Function notation and evaluation
Practise function notation and evaluation for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Use f(x), substitute values, interpret outputs and connect functions to graphs.
Before you start
- Substitute values into algebraic expressions accurately.
- Know that f(3) means the output when x = 3
- Read graph coordinates as input and output pairs.
Explanation
Function notation names a rule. If f(x) = 2x² − 5x + 1, then f(3) means replace every x with 3.
At Higher level, notation also supports composite and inverse functions, so keep the input-output order clear.
Method and rules
- f(a) means substitute x = a
- If f(x) = y, then x is the input and y is the output.
- A point (a, b) on y = f(x) means f(a) = b.
Worked examples
Worked example 2
Use a function value
For g(x) = 4x − 7, solve g(x) = 9.
- Write 4x − 7 = 9
- Add 7 to both sides.
- Divide by 4.
So: x = 4
Worked example 3
Interpret from a graph
A graph of y = f(x) passes through (2, 5). State f(2).
- The x-coordinate is the input.
- The y-coordinate is the output.
Answer: f(2) = 5
Watch out
- Writing f(3) as f × 3
- Substituting into only one occurrence of x.
- Forgetting brackets when substituting a negative value.
Related Higher Maths topics
Continue with the methods that connect most closely to this topic.