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
Back to Higher Mathematics
Higher Mathematics
Function notation and evaluation
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.
Visual support
Method and rules
- f(a) means substitute x = a
- If f(x) = y, then x is the input and y is the output.
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.
Exam reminder
Higher exam questions usually reward method setup before the final value. State the rule you are using, keep exact values where possible and check that the answer matches the question wording.