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Reference: Pearson Edexcel International A Level Pure Mathematics 3 Student Book. This chapter teaches you to think of a function as a rule with inputs, outputs, a domain, and a graph.
Main skills from this lesson
A function takes an input and gives one output. The domain tells you which inputs are allowed, and the range tells you possible outputs.
For composite functions, read from the inside out:
They are usually not the same.
input -> g -> f -> output
Before finding an inverse, check whether the function is one-to-one on its domain.
The modulus |x| means distance from zero, so it is never negative.
For y = |f(x)|:
For y = f(|x|):
|negative| = positive |-4| = 4
Modulus graph questions become easier when you sketch the original graph first.
An inverse function reverses the original function. A common method:
Transformations are instructions for moving graphs.
Study tip: horizontal transformations often feel reversed, so test with a simple point.
point (x, y) -> transformed point
Continue with quizzes, flashcards, or games when you are ready.