Guide
Functions/graphs have appeared repeatedly and CAT often tests domain, range, composition and structure rather than formula memorisation. For CAT preparation, the useful question is not “Have I finished the chapter?” but can I recognise the version of the concept CAT hides inside a word problem and choose an efficient method under time pressure?
What to know
The core checklist for this topic is: Domain/range, one-one/onto, composition, inverse, piecewise, transformations; and graphs, floor/fractional part basics, maxima/minima. Learn these as connected ideas rather than isolated formulas. CAT often combines two of them in one question.
Recurring CAT-style forms
Expect questions built around f(g(x)), inverse conditions, domain of composite, fixed points, piecewise count, and graph intersections. The wording changes, but the mathematical structure repeats. Your first 20–30 seconds should be spent identifying that structure before writing equations.
Decision rules worth remembering
- Domain of composite must satisfy inner and outer domains
- inverse requires suitable one-one restriction
- graph transformations shift/reflect/scale
One original example
If f(x)=2x+3, then y=2x+3 gives x=(y−3)/2. Therefore f⁻¹(x)=(x−3)/2. The inverse exists because the linear function is one-to-one.
The point of a worked example is not the answer; it is the choice of representation. After solving, ask whether a ratio table, base-100 assumption, sign chart, factorisation or diagram made the work shorter.
Common traps
- Assuming every function has inverse
- ignoring restricted domain
- confusing f²(x) with f(f(x))
- treating graph sketch as exact scale
These traps are valuable because they explain why a student can “know the formula” and still lose marks. Add the exact mistake to your error log when it occurs; do not simply write “silly mistake.”
How to practise
Start with 10–15 untimed questions until the first step becomes automatic. Then use mixed timed sets where this topic is not announced in advance. Finish with sectionals and mock review. Mastery checkpoint: Can determine domain/range and interpret a simple transformed graph without plotting many points.
Once that checkpoint is stable, move on rather than over-polishing one chapter. CAT QA is a portfolio of scoring areas; the objective is enough reliable topics to make question selection easy on exam day.
Preparing for CAT?
See where you actually stand before changing your shortlist or study plan.
Why On Your Mocks?
A mock score tells you what happened. OYM helps you understand what went wrong and what to work on next.