CAT Functions & graphs Questions

A function assigns an output to each allowed input. Function questions connect algebraic rules with domains, ranges and graphs, including composite and inverse functions.

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Key concepts

• Domain and range
• Composition and inverse functions
• Intercepts, symmetry and graph transformations

CAT functions & graphs practice questions

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Common mistakes

• Using inputs outside the domain.
• Treating an inverse function as the reciprocal of a function.

Practical solving approaches

• Establish the domain before simplifying or composing functions.
• Mark intercepts and turning points on a sketch, then check the intervals relevant to the question.

Functions & graphs FAQs

When does a function have an inverse?

An inverse is a function when the original function is one-to-one on the chosen domain. Restricting the domain can make an inverse possible.

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CAT Functions & graphs Questions

A function assigns an output to each allowed input. Function questions connect algebraic rules with domains, ranges and graphs, including composite and inverse functions.

3 free practice questions

Key concepts

• Domain and range
• Composition and inverse functions
• Intercepts, symmetry and graph transformations

CAT functions & graphs practice questions

Question 1Type in the answerMEDIUM

Question 1

Type in your answer in the input box provided below the question.

Answer each of the questions independently of each other.

f(1, y) = y + 1; f(0, y + 2) = f(1, y); f(x + 2, y + 2) = f(x, f(0, y + 2). Find the value of f(2, 4)

Your answer

Check answerView solution

Question 2Multiple choiceMEDIUM

Question 2

Select the correct alternative from the given choices

If f(x) = x – a, then f(f(f(x))) is:

Choose an answer

A.x - a B.x - 3aC.3x - 3aD.3x - a

Check answerView solution

Question 3Multiple choiceMEDIUM

Question 3

Select the correct alternative from the given choices

Choose an answer

A.1B.

C.

D.27

Check answerView solution

Common mistakes

• Using inputs outside the domain.
• Treating an inverse function as the reciprocal of a function.

Practical solving approaches

• Establish the domain before simplifying or composing functions.
• Mark intercepts and turning points on a sketch, then check the intervals relevant to the question.

Functions & graphs FAQs

When does a function have an inverse?

An inverse is a function when the original function is one-to-one on the chosen domain. Restricting the domain can make an inverse possible.

More Algebra practice

• Inequalities & modulus →
• Linear equations & word problems →
• Logarithms, indices & surds →
• Polynomials, higher-degree equations & binomial expansion →
• Quadratic equations & expressions →
• Sequences & series →