Grade 10 Maths · Trigonometry · Shift a graph

Shifting Graphs Grade 10

Slide a graph left, right, up or down and write its new equation (for example moving y = x^2 two units right gives y = (x - 2)^2).

questions use it, all grades · 39 past paper, 82 practice: 121 questions use it, all grades · 39 past paper, 82 practice
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Functions : Horizontal Translations - Horizontal Shift - y = f(x - c) Examples and ExplanationRadford Mathematics

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

Horizontal Translation of Quadratic Functions - NerdstudyNerdstudy

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Question 6.3 · November 2025 · Paper 1 · National (DBE) · 2 marks

The graphs of

g (x) = x + c

and

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

are drawn below. Graph

g

and the vertical asymptote of

f

intersect at the

x

-axis. $Diagram for this question$

6.3 Describe the transformation that

g

must undergo to become an axis of symmetry of

f

that cuts

f

at two points.(2)

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

More past paper questions: shift a graph

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

3. Question 4.1.3 · November 2022 · Paper 1 · National (DBE) · 2 marks
4.1 Sketched below is the graph of $h (x) = \frac{1}{x + p} + q$ . The asymptotes of $h$ intersect at $(1; 2)$ .

Answer the questions that follow. $Diagram for question 4.1$
4.1.3 Write down the $x$ -coordinate of the $x$ -intercept of $g$ if $g (x) = h (x + 3)$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  $- 3$ $x = \frac{1}{2} - 3$
  1 mark · Shift a graph
2. ✓
  $x = - \frac{5}{2}$ $= - \frac{5}{2}$
  1 mark · Shift a graph
4. Question 4.3.1 · May/June 2022 · Paper 1 · National (DBE) · 2 marks
The graph of $g (x) = a (\frac{1}{3})^{x} + 7$ passes through point $E (- 2; 10)$ .
4.3 Consider: $h (x) = (\frac{1}{3})^{x}$

Answer the following.
4.3.1 Describe the translation from $g$ to $h$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  1 unit right $g (x) = (\frac{1}{3})^{x + 1} + 7$
  Translation by $1$ unit to the right
  1 mark · Shift a graph
2. ✓
  7 units downwardsand $7$ units downwards
  1 mark · Shift a graph
5. Question 6.6 · November 2018 · Paper 2 · National (DBE) · 2 marks
The graphs of the functions $f (x) = a cos b θ$ and $g (x) = c tan θ$ for $x \in [- 180°; 180°]$ are sketched below. The graphs intersect at P $(58°; 1, 6)$ and Q. $Diagram for this question$
6.6 If the system of axes is shifted $45°$ to the left and the graphs remain fixed, write down the equation that is now represented by graph $f$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  3 $f (x) = 3 cos (θ - 45°)$ : amplitude 3
  1 mark · Shift a graph
2. ✓
  $- 45°$ $f (x) = 3 cos (θ - 45°)$
  1 mark · Shift a graph
6. Question 7.5 · May/June 2025 · Paper 2 · National (DBE) · 2 marks
In the diagram, the graphs of $f (x) = 2 cos x + 1$ and $g (x) = sin 2 x$ are drawn for the interval $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
7.5 Graph g is shifted $4 5^{\circ}$ to the right to obtain a new graph h.

Determine the equation of h in its simplest form.(2)
Show the memo (2 ticks)Memo
1. ✓
  Apply the horizontal shift transformation $g (x) = sin 2 x$
  Shift $4 5^{\circ}$ to the right means substituting $(x - 4 5^{\circ})$ for $x$ :
  $h (x) = sin 2 (x - 4 5^{\circ})$
  $h (x) = sin (2 x - 9 0^{\circ})$
  1 mark · Shift a graph
2. ✓
  Simplify using reduction formulae and co-ratios $h (x) = sin [- (9 0^{\circ} - 2 x)]$
  $h (x) = - sin (9 0^{\circ} - 2 x)$
  $h (x) = - cos 2 x$
  1 mark · Use a reduction formula

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