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What you will learn in Sets, Relations & Functions
1. Sets, Notation and Subsets
Roster, set-builder and interval notation — three ways of writing the same collection, each better at something.
2. Set Operations and Venn Diagrams
Shade a region and the expression appears; count it and the double-count inclusion–exclusion corrects becomes visible.
3. Cartesian Products and the Plane
Ordered pairs as the bridge from sets to coordinates — the plane is a product before it is a picture.
4. Relations, Domain and Range
A relation is any subset of a product. Reflexive, symmetric and transitive are the three properties worth naming, and each fails for a reason you can point at.
5. What Makes a Function
Exactly one arrow out of every input. The vertical-line test is that sentence, drawn.
6. Domains, Ranges and Restrictions
Domain as a property you discover by probing: feed the machine a value it cannot take and it refuses with a reason.
7. Injective, Surjective, Bijective
Three words for three ways the arrows can land, and the reason an inverse needs all of them at once.
8. Composition and Inverse Functions
Two machines wired in series, and the mirror in y = x that turns one into the other when it is allowed to.
9. Transformations of Graphs
Translation, stretch and reflection — and why reordering the stack changes the answer.
10. Exponential Functions, Growth and Decay
A constant ratio rather than a constant difference, on an axis where it straightens into a line — and e, arriving as a limit you watch appear.
11. Logarithms as Inverses, and Their Laws
The inverse of an exponential, three laws that are statements about adding lengths, and the scales — pH among them — that are built on it.