Free Year 12 Functions Quiz — 10 Questions, Instant Results

Free practice quizzes › Year 12 Maths (VCE) quiz › Functions

What Year 12 students need to know about functions

A short orientation first. Year 12 functions covers polynomial, exponential, logarithmic and circular functions, transformations, composite and inverse functions, and solving equations involving them exactly and numerically.

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 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 misconceptions RHZ tutors correct most often with Year 12 students:

• The inverse function is confused with the reciprocal.
• A composite function is formed in the wrong order.
• The domain of a composite function is not restricted.

Each of these is fixable in a session or two once it has been named, which is why the results panel below shows the correct answer and an explanation rather than just a score.

How to practise functions at home

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

1. Use the CAS to check exact solutions.
2. Sketch each function family with all key features.
3. Find inverses by swapping and solving, then check with a composite.

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

Every set on this page is a seeded selection of 10 from the 17 functions questions that pass our quality gate. A different seed gives a different set, and there are many more combinations than any one student will need. The correct answers never appear in the page source; the browser asks our server for them after you press Mark my answers.

A single-topic quiz is more precise than a mixed one: if the score here is low, the gap is in functions, not somewhere in Year 12 maths generally. It is still short, though, and it cannot show how a student copes with the stretch and challenge questions that decide a top result. That is what the free Skills Check adds.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 81656 · New set of questions →

Question 1

Functions

y = f(x) − 3 shifts the graph?

left 3 right 3 up 3 down 3

Question 2

Functions

The turning point of y = x² is?

(0, 1) (1, 0) (0, 0) (1, 1)

Question 3

Functions

Let f: R → R and g: R → R be defined by f(x) = eˣ and g(x) = ln(x² + 1). Consider the composite function f(g(x)). Which of the following correctly states f(g(x)) and its range?

f(g(x)) = e^(ln(x² + 1)) = x, range R f(g(x)) = ln(eˣ² + 1), range R f(g(x)) = x² + 1, range [1, ∞) f(g(x)) = x² + 1, range (0, ∞)

Question 4

Functions

The period of y = cos(x) is?

2π 1 π π/2

Question 5

Functions

y = 2f(x) does what to the graph vertically?

shifts it up reflects it stretches it shifts it down

Question 6

Functions

Let f(x) = 2x − 1 and g(x) = x² + 3. If h(x) = f⁻¹(g(x)), which of the following is h(x)?

1/(2(x² + 3) − 1) (x² + 3 − 1)/2 (x² + 4)/2 2(x² + 3) − 1

Question 7

Functions

The function f: [−1, 3] → R is defined by f(x) = −x² + 2x + 3. What is the range of f?

[−6, 3] [−6, 4] [0, 4] [−5, 4]

Question 8

Functions

y = 1/x has a vertical asymptote at?

y = 1 x = 1 x = 0 x = −1

Question 9

Functions

A function g is defined by g(x) = 2/(x + 1) + 3. Which statement about g is correct?

g has a vertical asymptote at x = −1 and a horizontal asymptote at y = 3. g has a vertical asymptote at x = 1 and a horizontal asymptote at y = 3. g has no asymptotes because of the constant term +3. g has a vertical asymptote at x = −1 and a horizontal asymptote at y = 0.

Question 10

Functions

The function f: R → R is defined by f(x) = x³ − 3x. On which interval(s) is f strictly decreasing?

(−∞, −1) ∪ (1, ∞) (0, ∞) (−1, 1) (−√3, √3)

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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 Maths topics for Year 12

Mixed Year 12 Maths (VCE) quiz (all topics) →

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