Grade 11 Maths · Functions · Paper 1

Translations and Reflections of Graphs Grade 11

Real Translations and Reflections of Graphs past paper questions and answers from 2023 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 9 past paper questions
skills: 4 skills
videos: 4 videos

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Question 5.4 · November 2025 · Paper 1 · Provincial · 3 marks

The graphs of

f (x) = \frac{a}{x + p} + q

and

g (x) = \frac{x}{3} + c

are drawn below. C

(3; - 1)

is the point of intersection between the asymptotes of

f

. A and B are

x

- and

y

-intercepts of

f

and

g

respectively. E

(4; 2)

is a point on

f

in the first quadrant. $Diagram for this question$

5.4 Write down the domain of

h

, if

h (x) = f [- (x - 4)]

(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Translations and Reflections of Graphs skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Translations and Reflections of Graphs Grade 11 questions and answers

Try each one on paper before you open the memo.

4. Question 6.3 · November 2024 · Paper 2 · Provincial · 2 marks
The graph of $f (x) = cos (x + 30°)$ in the interval of $x \in [- 120°; 150°]$ has been drawn in the diagram below. $Diagram for this question$
6.3 Write down the equation of $h$ in its simplest form.(2)
Show the memo (2 ticks)Memo
1. ✓
  $cos (90° + x)$ $h (x) = cos (x + 60° + 30°) + 1 = cos (90° + x) + 1$
  1 mark · Shift a graph
2. ✓
  $- sin x$ $h (x) = - sin x + 1$
  1 mark · Use co-ratio identities
5. Question 5.5 · November 2024 · Paper 1 · Provincial · 3 marks
The lines $y = - x + 4$ and $y = x - 2$ are the axes of symmetry of the function $f (x) = \frac{- 3}{x + p} + q$ .
5.5 Write down the domain of $g$ if $g$ is the reflection of $f$ along the line $x = 0$ .(3)
Show the memo (2 ticks)Memo
1. ✓
  Vertical asymptoteVertical asymptote of $g$ (by inspection): $x = - 3$
  
  OR: $g (x) = f (- x) = \frac{- 3}{- x - 3} + 1$ ; $- x - 3 = 0$ ; $x = - 3$
  1 mark · Reflect a graph
2. ✓
  Domain $∴ x \in R; x \neq = - 3$
  2 marks · State the domain and range
6. Question 6.4 · November 2024 · Paper 1 · Provincial · 3 marks
Sketched below is the graph of $f (x) = x^{2} - 4 x - 5$ for $x \in (- \infty; 6]$ .

A and B are the $x$ -intercepts and C the $y$ -intercept of $f$ . $Diagram for this question$
6.4 Write down the equation of $g$ in the form $g (x) = a x^{2} + b x + c$ , if it is given that $g (x)$ is obtained by shifting $f (x)$ two units to the right and five units up.(3)
Show the memo (3 ticks)Memo
1. ✓
  $(x - 2)$ $g (x) = (x - 2)^{2} - 4 (x - 2) - 5 + 5$
  1 mark · Shift a graph
2. ✓
  $+ 5$ $... + 5$
  1 mark · Shift a graph
3. ✓
  Answer $= x^{2} - 4 x + 4 - 4 x + 8 - 5 + 5$
  $= x^{2} - 8 x + 12$
  1 mark · Collect like terms
7. Question 5.7 · November 2023 · Paper 1 · Provincial · 4 marks
The diagram below shows the graph of $f (x) = \frac{a}{x + p} + q$ . The asymptotes of $f$ intersect at $(- 3; - 1)$ and $f$ cuts the $x$ -axis at $x = - 5$ . $Diagram for this question$
5.7 Describe the transformation of $f$ to $g$ , given that $g (x) = \frac{2}{x - 1} + 1$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Reflected $f$ is reflected ...
  1 mark · Reflect a graph
2. ✓
  $x$ -axis... in the $x$ -axis ...
  1 mark · Reflect a graph
3. ✓
  4 units... and then shifted 4 units ...
  1 mark · Shift a graph
4. ✓
  Right... to the right.
  1 mark · Shift a graph

Translations and Reflections of Graphs Grade 11 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Introduction to TRANSFORMATION in Mathematics - Grade 8SHFT - Your Learning

Grade 12 Functions Student Question Find equation of p(x) if f(x) is shifted 2 units left | NTENTE \ New Technological Education

Functions : Horizontal Translations - Horizontal Shift - y = f(x - c) Examples and ExplanationRadford Mathematics

Reflections of the Exponential GraphMaths101 with Jana van Niekerk

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