Grade 12 · Mathematics

Understand function notation and substitution

A function assigns exactly one output to each allowed input. In Grade 12 Mathematics, f(x) names the output associated with x; it does not mean f multiplied by x. Substituting carefully is the starting point for interpreting graphs, finding intercepts and comparing functions. Use brackets around negative inputs so that powers and signs are evaluated correctly.

Original explanation prepared with AI assistance.

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What you will practise

Interpret f(x) and substitute negative inputs correctly.

The method

Replace every occurrence of x with the chosen input. Evaluate powers before multiplication, then addition and subtraction.

Worked example

If f(x) = x² − 3x + 2, find f(−2).

Substitute with brackets: f(−2) = (−2)² − 3(−2) + 2.
The squared term is 4 and −3(−2) = 6.
Therefore f(−2) = 4 + 6 + 2 = 12.
The point (−2; 12) lies on the graph of f.

Common mistake

Writing −2² instead of (−2)² changes the squared term from 4 to −4.

Try it yourself

For g(x) = 2x² + x − 1, find g(−1).

Show the explained solution

g(−1) = 2(−1)² + (−1) − 1 = 2 − 1 − 1 = 0.

Curriculum and sources

Use the official CAPS subject document and your teacher’s annual plan to confirm the sequence and scope for your class. The link below is an official reference, not evidence of DBE approval of this explanation.

DBE: CAPS for the FET phase

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