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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Functions & graphs

How often Functions & graphs comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 4 of the last 5 Higher Level papers, most recently in 2026. most years

OL Asked on 2 of the last 5 Ordinary Level papers, most recently in 2026.

Functions & graphs, Higher Level(7 marks)

Quick ones on Functions & graphs.

(a)f(x) = 3x − 2. Find f(−4).
  1. 10
  2. −14
  3. −10
(b)A relation maps 2 → 5 and 2 → 7. Is it a function?
  1. Yes: 5 and 7 are both outputs
  2. Yes: every input has an output
  3. No: 2 has two outputs
(c)f: x → x², with domain {−2, −1, 0, 1, 2}. What is the range?
  1. {0, 1, 4}
  2. {0, 1, 2}
  3. {−4, −1, 0, 1, 4}
Show the answers

(a) −14

(b) No: 2 has two outputs

(c) {0, 1, 4}

Your turn: Higher Level questions on Functions & graphs.

Higher Level

Asked on 4 of the last 5 Higher Level papers, most recently in 2026. most years

Every paper, year by year

YearWhere it came up
2026Q6, Q8
2025Q9, Q12
2024Q8
2023Q11
2022Not asked

Links open the State Examinations Commission’s paper for that year.

More Functions & graphs questions

Functions & graphs, 2 marks

Where does the graph of y = 2ˣ cut the y-axis?

  1. (0, 0)
  2. (0, 2)
  3. (0, 1)
Show the answer

(0, 1)

On the y-axis x = 0, and 2⁰ = 1 (any non-zero number to the power 0 is 1). So the graph of y = 2ˣ passes through (0, 1).

Ordinary Level

Asked on 2 of the last 5 Ordinary Level papers, most recently in 2026.

Every paper, year by year

YearWhere it came up
2026Q12
2025Not asked
2024Not asked
2023Q7
2022Not asked

Links open the State Examinations Commission’s paper for that year.

More Functions & graphs questions

Functions & graphs, 2 marks

f(x) = 3x − 2. Find f(4).

  1. 14
  2. 12
  3. 10
Show the answer

10

Replace x with 4: f(4) = 3(4) − 2 = 12 − 2 = 10.

Functions & graphs, 2 marks

What is the set of inputs of a function called?

  1. The co-domain
  2. The domain
  3. The range
Show the answer

The domain

The domain is the set of inputs (x values). The range is the set of outputs you actually get, and the co-domain is where outputs may come from.

Functions & graphs, 3 marks

Why is {(1, 2), (1, 5), (3, 4)} not a function?

  1. The input 1 has two outputs
  2. The outputs are not in order
  3. The input 2 is missing
Show the answer

The input 1 has two outputs

In a function every input has exactly ONE output. Here the input 1 goes to both 2 and 5, so it is not a function.

Other Maths topics

All of Junior Cycle Maths