Free · Year 3 of high school · 50 minutes · 15 questions · no penalty

Practice maths class test — Year 3: functions and transformations of graphs.

15 questions drawn at random from a bank of 25, on the block of the programme your teacher is finishing: every attempt is a different test. No penalty for wrong answers, so answer even if you are not sure. At the end you receive by email the correct answer to every question and your weak topics — with an account you see them straight away here on the page. The step-by-step solution unlocks with your first lesson.

A class test is the written test an Italian high-school class sits after each block of the programme; this practice version is multiple choice.

Test in ItalianThe questions of this simulator are in Italian, as in the real exam.

Test prepared by Gaetano Livornese · Aerospace engineer, Politecnico di Milano · maths and physics tutor · updated 13 October 2026

Programme covered by the test

Domain of rational and radical functions
Injective, surjective and bijective functions
Composite and inverse functions
Translations, reflections and dilations of a graph
Piecewise functions and absolute value

Two worked examples from the test

Question 1 · Funzioni: dominio, composta, inversa, trasformazioni di grafici · Geometria analitica e funzioni

Determina il dominio della funzione

$f (x) = \frac{2 x - 5}{x + 4}$

A $R ∖ {- 4}$ correct answer
B $R ∖ {4}$
C $R ∖ {\frac{5}{2}}$
D $R$

Solution

La funzione è razionale fratta: l'unica condizione di esistenza è che il denominatore non si annulli.
Impongo $x + 4 \neq = 0$ .
Ottengo $x \neq = - 4$ .
Il numeratore non pone condizioni: per $x = \frac{5}{2}$ la funzione esiste e vale $0$ .
Dominio: $R ∖ {- 4}$ .

Question 2 · Funzioni: dominio, composta, inversa, trasformazioni di grafici · Geometria analitica e funzioni

Determina il dominio della funzione

$f (x) = \frac{x}{x ^{2} - 5 x + 6}$

A $R ∖ {- 2, - 3}$
B $R ∖ {0, 2, 3}$
C $R ∖ {2, 3}$ correct answer
D $R ∖ {5, 6}$

Solution

Condizione di esistenza: $x^{2} - 5 x + 6 \neq = 0$ .
Scompongo con somma e prodotto: $x^{2} - 5 x + 6 = (x - 2) (x - 3)$ .
Il prodotto si annulla per $x = 2$ e $x = 3$ : sono i valori da escludere.
Il numeratore $x$ non dà condizioni: $x = 0$ appartiene al dominio e lì $f (0) = 0$ .
Dominio: $R ∖ {2, 3}$ .

In the online practice test you will find 13 more questions like these; the correct answer to every question arrives by email.

Prefer paper? Download the test as a PDF (15 questions, 4 pages · 85 KB, ready to print). You receive the solutions by email after taking it online.

Download the PDF

What a maths test on functions and graphs looks like

Domains of functions with fractions and radicals, a composite function and its inverse, recognising injectivity and surjectivity, and a graph to transform with translations, reflections or absolute value.

The mistake that costs the grade

In the domain, putting only the condition from the root and forgetting the denominator (or the other way round): all the conditions must be written and then intersected. In composites, swapping the order — f(g(x)) and g(f(x)) are different functions with different domains.

How to use this practice test

Take it once cold, without revising and with the timer on: it is there to show you where you stand, not to look good. Then look at your weak topics, revise only those — usually two or three, not the whole chapter — and retake it after a few days. The 15 questions are drawn from a bank of 25, so the second attempt is not the same test and the scores are genuinely comparable.

Is the score not enough?

See which topics lost you the most marks, then read how to handle test anxiety — or we look at your results together: the diagnostic is free.

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