Leaving Cert Maths: Functions
How often Functions comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
FL Asked on 7 of the last 7 Foundation Level papers, most recently in 2026. banker
Quick ones on Functions.
- −5
- −3
- 5
- f⁻¹(x) = 1/(x − 4)
- f⁻¹(x) = 4 − x
- f⁻¹(x) = x + 4
- injective (one-to-one)
- continuous
- surjective (onto)
Show the answers
(a) −3
(b) f⁻¹(x) = x + 4
(c) injective (one-to-one)
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q8, Q10 |
| 2025 | Q2 |
| 2024 | Q8, Q10 |
| 2023 | Q2, Q5, Q9 |
| 2022 | Q7 |
| 2021 | Q8 |
| 2019 | Q2, Q9 |
| 2018 | Q6, Q7, Q8 |
| 2017 | Q1, Q5, Q6, Q9 |
| 2016 | Q3, Q5, Q8 |
Links open the State Examinations Commission’s paper for that year.
More Functions questions
Functions, 2 marks
The function f(x) = x³, x ∈ ℝ, is …
- not injective
- undefined for x < 0
- injective (one-to-one)
Show the answer
injective (one-to-one)
x³ is always increasing, so no two different inputs give the same output. Any horizontal line cuts it only once.
Functions, 2 marks
g(x) = 2ˣ. What is g(−1)?
- 0
- ½
- −2
Show the answer
½
g(−1) = 2⁻¹ = 1/2. A negative index means 1 over.
Functions, 2 marks
The graph of y = f(x − 2) is the graph of f moved …
- right 2 units
- left 2 units
- up 2 units
Show the answer
right 2 units
f(x − 2) takes at x the value f had at x − 2, so every point moves 2 units right. The minus sign moves it right.
Ordinary Level
Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q6, Q8, Q10 |
| 2025 | Q5, Q7, Q8 |
| 2024 | Q6, Q7, Q8, Q9 |
| 2023 | Q4, Q7, Q9 |
| 2022 | Q4, Q5, Q7, Q9, Q10 |
| 2021 | Q5, Q8 |
| 2019 | Q3, Q7, Q9 |
| 2018 | Q5, Q8 |
| 2017 | Q3, Q8, Q9 |
| 2016 | Q4, Q8, Q9 |
Links open the State Examinations Commission’s paper for that year.
More Functions questions
Functions, 2 marks
f(x) = 2x + 1. Find f(3).
- 6
- 9
- 7
Show the answer
7
Put 3 in place of x: f(3) = 2(3) + 1 = 6 + 1 = 7.
Functions, 2 marks
f(x) = x² − 4. Find f(0).
- 0
- −4
- 4
Show the answer
−4
f(0) = 0² − 4 = 0 − 4 = −4.
Functions, 2 marks
Where does the graph of y = 3x + 6 cross the y-axis?
- (0, 6)
- (6, 0)
- (0, 3)
Show the answer
(0, 6)
On the y-axis x = 0, so y = 3(0) + 6 = 6. The point is (0, 6).
Foundation Level
Asked on 7 of the last 7 Foundation Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q5, Q6, Q9 |
| 2025 | Q9 |
| 2024 | Q3 |
| 2023 | Q6, Q9 |
| 2022 | Q11 |
| 2021 | Q9 |
| 2019 | Q5, Q7 |
Links open the State Examinations Commission’s paper for that year.
More Functions questions
Functions, 2 marks
On a distance-time graph, a flat (horizontal) part of the line means …
- The person is moving fastest
- The person is going back home
- The person is stopped
Show the answer
The person is stopped
A flat line means the distance is not changing as time goes on, so the person is not moving.
Functions, 2 marks
A taxi charges €4 plus €2 per km. What is the cost of a 5 km trip?
- €11
- €14
- €30
Show the answer
€14
5 km at €2 is €10. Add the €4 starting charge: €10 + €4 = €14.
Functions, 2 marks
A plant is 10 cm tall. It grows 3 cm each week. How tall is it after 4 weeks?
- 22 cm
- 17 cm
- 52 cm
Show the answer
22 cm
4 weeks × 3 cm = 12 cm of growth. 10 + 12 = 22 cm.