Grade 10 Maths · Functions

Reflect a graph

Flip a graph in the x-axis or y-axis and write the new equation (for example reflecting y = 2ˣ in the x-axis gives y = −2ˣ).

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Reflections of the Exponential GraphMaths101 with Jana van Niekerk

Reflection Parabola in Y axis | Grade 11 FunctionsKevinmathscience

Reflections of a Function - NerdstudyNerdstudy

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Question 5.3 · November 2024 · Paper 1 · Provincial · 2 marks

5.3 The graph of

h (x) = x^{2} - 4

is obtained by transforming the graph of f. Describe the transformation that maps the graph of f onto the graph of h.(2)

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

More past paper questions: reflect a graph

Work each one out first, then open the memo and check every tick.

3. Question 6.5 · May/June 2024 · Paper 1 · National (DBE) · 5 marks
The graphs of $f (x) = x^{2} - 2 x - 3$ and $g (x) = m x + c$ are drawn below. D and E are the $x$ -intercepts and P is the $y$ -intercept of $f$ . The turning point of $f$ is T $(1; - 4)$ . The graphs of $f$ and $g$ intersect at P and E.
6.5 Determine the maximum vertical distance between $h$ and $g$ if $h (x) = - f (x)$ for $x \in [- 2; 3]$ .(5)
Show the memo (5 ticks)Memo
1. ✓
  Equation of h $h (x) = - x^{2} + 2 x + 3$
  1 mark · Reflect a graph
2. ✓
  Distance between the graphs $D = - x^{2} + 2 x + 3 - (x - 3) = - x^{2} + x + 6$
  1 mark · Find a horizontal or vertical length
3. ✓
  Method for the maximum $D^{'} (x) = - 2 x + 1 = 0$ or $x = - \frac{b}{2 a} = - \frac{1}{2 ( - 1 )}$
  1 mark · Find turning point of a parabola
4. ✓
  x-value $x = \frac{1}{2}$
  1 mark · Find turning point of a parabola
5. ✓
  Maximum distance $D (\frac{1}{2}) = - (\frac{1}{2})^{2} + \frac{1}{2} + 6 = 6, 25$ units
  1 mark · Find turning point of a parabola
4. Question 5.7.1 · November 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, the graphs of $f (x) = cos x + a$ and $g (x) = b sin x$ are drawn for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
5.7 The graph of f is reflected about the x-axis and then moved 2 units downwards to form the graph of h. Determine:
5.7.1 The equation of h(2)
Show the memo (2 ticks)Memo
1. ✓
  Reflection: −cos xReflect in the $x$ -axis: $y = - (cos x + 1) = - cos x - 1$ | $h (x) = - cos x \dots$
  1 mark · Reflect a graph
2. ✓
  Shift down 2: −3 $h (x) = - cos x - 1 - 2 = - cos x - 3$
  1 mark · Shift a graph
5. Question 7.6 · November 2024 · Paper 1 · Provincial · 2 marks
The graphs of $f (x) = - (b)^{x} + 8$ and $g (x) = \frac{3}{2} x + 7$ are drawn below.

A $(- 2; 4)$ and B are points of intersection of $f$ and $g$ . B is the $y$ -intercept of both graphs $f$ and $g$ . $Diagram for this question$
7.6 Describe the transformation of $f$ to $h$ if $h (x) = (\frac{1}{2})^{x} - 5$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Reflection along $x$ -axisReflection along $x$ -axis:
  $- f (x) = (\frac{1}{2})^{x} - 8$
  1 mark · Reflect a graph
2. ✓
  3 units upwardsthen, vertical translation by 3 units upwards:
  $h (x) = (\frac{1}{2})^{x} - 8 + 3 = (\frac{1}{2})^{x} - 5$
  1 mark · Shift a graph
6. 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

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