Free Year 12 Functions & graphs Quiz — 10 Questions, Instant Results

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What Year 12 students need to know about functions and graphs

A short orientation first. In Units 3 and 4 functions and graphs covers exponential, logarithmic and circular functions, transformations described by matrices, composite and inverse functions and the graphs of derivatives.

Our tutors wrote and checked these questions against the VCE study design, which is why the wording and the difficulty match what a Year 12 student meets at school.

The usual functions and graphs errors at Year 12

If your child gets a question wrong here, it is worth checking whether one of these is behind it. They are the functions and graphs misconceptions RHZ tutors correct most often with Year 12 students:

• Transformations are applied in the wrong order.
• Domain and range are stated for the wrong function.
• An inverse is drawn without restricting the domain.

None of these is a sign of low ability. Each is a reasonable idea that worked in an earlier year and needs replacing, which is exactly what a good explanation, or a tutor, does.

How to practise functions and graphs at home

Practice works when it is short, regular and specific. For functions and graphs, our tutors suggest:

1. Use the CAS to confirm sketches.
2. Sketch each family by hand with all key features labelled.
3. Practise transformations one step at a time.

For VCE maths, fluency in the foundations frees up working memory for the extended questions. Do a short mixed set daily and a timed paper each fortnight.

About the questions on this page

The 10 questions are drawn from 13 eligible items on functions and graphs in our Year 12 Mathematical Methods bank, all at the easy and at-level tiers. The selection is fixed for this address so a shared link shows the same quiz; press New set of questions or add ?seed= to the address for a different mix. Options are shuffled, no two questions share a stem, and the answer key is fetched from our server only after you submit, so it is not hidden in the page.

Because every question here is on functions and graphs, a low score is a clear signal and a high score is genuinely reassuring for this topic. What it cannot tell you is whether the other Year 12 Mathematical Methods topics are equally secure, or how far above the year level the student can go; the free Skills Check covers both.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 75082 · New set of questions →

Question 1

Functions & graphs

The function g : R → R is defined by g(x) = x³ − 6x. Which statement is true?

g has exactly one x-intercept g has a local maximum at x = −√2 and a local minimum at x = √2 g is increasing on (−√2, √2) and has no points of inflection g is concave up for all x > 0

Question 2

Functions & graphs

Let f(x) = ln(x² − 5x + 6). What is the domain of f?

2 < x < 3 x < 2 or x > 3 all real x except x = 2 and x = 3 x > 3

Question 3

Functions & graphs

The function f(x) = ln(x − 2) + 1 has a vertical asymptote and a domain. Which of the following correctly states both?

Vertical asymptote x = 2; domain (2, ∞) Vertical asymptote x = 2; domain [2, ∞) Vertical asymptote x = 1; domain (1, ∞) Vertical asymptote x = −2; domain (−2, ∞)

Question 4

Functions & graphs

If f(x) = x² − 1, find f(3).

5 8 9 10

Question 5

Functions & graphs

y = 1/x has a vertical asymptote at?

y = 0 x = 1 x = 0 x = −1

Question 6

Functions & graphs

The graph of y = f(x) is transformed to y = −f(2x) + 3. A point (4, 1) on the original graph maps to which point on the transformed graph?

(2, 2) (4, 2) (8, 2) (2, −2)

Question 7

Functions & graphs

Evaluate log₂(8).

16 2 4 3

Question 8

Functions & graphs

Let f(x) = 2x − 1 and g(x) = x² + 3. What is the domain of the composite function f(g(x))?

x ≠ 0 x ≥ 0 All real numbers x > −3

Question 9

Functions & graphs

If f(x) = x + 4, the inverse f⁻¹(x) is?

4 − x 1/(x+4) x + 4 x − 4

Question 10

Functions & graphs

y = f(x) + 2 shifts the graph?

down 2 left 2 right 2 up 2

Mark my answers →

Your result

0 / 10

Take the free full Skills Check →   Try another set

How to read a score out of 10

9 or 10 out of 10

The easy and at-level content is secure. The useful question now is how far above the year level the student can go, which a ten-item quiz cannot show. The free Skills Check adds stretch and challenge questions on every topic so you can see the ceiling as well as the floor.

7 or 8 out of 10

Solid, with one or two specific gaps. Look at which topic the incorrect answers came from (the results panel names the weakest topic) and spend a week on that topic before re-testing with a different seed.

5 or 6 out of 10

Some core ideas are shaky. The pattern matters more than the score: two misses in the same topic is a gap; misses scattered across topics usually means reading the question too fast. Either way, the Skills Check will tell you which.

4 or fewer out of 10

Foundations from an earlier year are probably missing, which is common and fixable. Try the quiz one year level down to confirm, then talk to a tutor about a short catch-up plan rather than more of the same practice.

What to do with the result

Questions? Call 03 9509 3293 or book a free consultation. RHZ Tutoring, 17/47 Apex Drive, Truganina VIC 3029.

Frequently asked questions

Other Mathematical Methods topics for Year 12

Mixed Year 12 Mathematical Methods quiz (all topics) →

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All 3,261 free practice questions, Prep to Year 12 →