Free Year 11 Functions & graphs Quiz — 10 Questions, Instant Results

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Functions & graphs at Year 11: what the curriculum expects

In Units 1 and 2 functions and graphs covers linear, quadratic, cubic and quartic polynomials, power functions, transformations, domain and range and inverse relations.

This topic sits inside the VCE study design for Year 11 Mathematical Methods; the questions stay at the easy and at-level tiers so the result is a fair check of the foundations.

Common functions and graphs misconceptions tutors see

The distractors in this quiz are built from real misconceptions rather than random wrong numbers, so a specific wrong answer usually points to a specific gap. The ones we see most at Year 11:

• Asymptotes are omitted from sketches.
• Transformations are applied in the wrong order.
• Domain and range are stated for the wrong function.

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.

Practising functions and graphs with a Year 11 student

The habits that move functions and graphs from shaky to secure at Year 11:

1. Sketch each family by hand with all key features labelled.
2. Practise transformations one step at a time.
3. Find inverses and check with composites.

At VCE, practise by hand for Exam 1 and with the CAS for Exam 2, use past papers under time and mark against the examiners' reports. Fix the errors the same week.

How this functions and graphs quiz works

We keep 11 functions and graphs questions for Year 11 that meet our standard, at the easy and at-level tiers, and this page serves 10 of them at a time. The default set is stable, so a teacher or parent can share the link; a fresh set is one click away. Marking happens on our server so the answer key cannot be read from 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 11 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 81656 · New set of questions →

Question 1

Functions & graphs

The function f: R → R is defined by f(x) = 2x² − 8x + 5. The function is written in the form f(x) = 2(x − h)² + k. What are the values of h and k?

h = 2, k = 5 h = 2, k = −3 h = 4, k = 5 h = −2, k = −3

Question 2

Functions & graphs

The range of f(x) = x² + 1 is?

y ≥ 1 y ≤ 1 y ≥ 0 all real y

Question 3

Functions & graphs

If f(x) = x² and g(x) = x + 1, find f(g(2)).

4 5 9 7

Question 4

Functions & graphs

The turning point of y = (x − 2)² + 3 is?

(2, −3) (2, 3) (3, 2) (−2, 3)

Question 5

Functions & graphs

y = (x − 1)(x + 4) cuts the x-axis at?

x = −1 and 4 x = 1 and 4 x = 1 and x = −4 x = 0

Question 6

Functions & graphs

If f(x) = 2x + 3, find f(4).

14 11 8 5

Question 7

Functions & graphs

The graph of y = f(x) has domain [−3, 5] and range [−1, 4]. What are the domain and range of y = f(−x) + 2?

Domain [−5, 3], range [1, 6] Domain [−3, 5], range [1, 6] Domain [−5, 3], range [−3, 2] Domain [3, −5], range [1, 6]

Question 8

Functions & graphs

The y-intercept of y = 3x − 5 is?

5 3 −3 −5

Question 9

Functions & graphs

The function f: R → R is defined by f(x) = x² − 6x + k. For f to have no x-intercepts, which condition on k is required?

k > 3 k < 3 k > 9 k < 9

Question 10

Functions & graphs

The domain of f(x) = √x is?

x ≥ 0 x > 0 x ≤ 0 all real x

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

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