Grade 12 Maths · Functions

Sketch an inverse graph

Draw the inverse of a graph by reflecting it in the line y = x (for example the inverse of y = 2ˣ is y = log₂ x).

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6) Inverse of exponential | Part 1Kevinmathscience

2) Inverse of straight lineKevinmathscience

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Question 5.2 · March 2024 · Paper 1 · Provincial · 4 marks

Given:

f (x) = 3 x^{2}

where

x \geq 0

5.2 On the same set of axes, draw the graphs of

f

and

f^{- 1}

showing the intercepts with the axes as well as coordinates of two points on each graph.(4)

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

More past paper questions: sketch an inverse graph

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

3. Question 4.2.2 · March 2025 · Provincial · 3 marks
4.2 Consider $g (x) = (\frac{1}{3})^{x}$ .
4.2.2 Draw a sketch graph of $g^{- 1}$ indicating any intercepts with the axes as well as one more point on the graph.(3)
Show the memo (3 ticks)Memo
1. ✓
  Draw shapeDecreasing log graph (in Q1 and Q4).
  1 mark · Sketch an inverse graph
2. ✓
  Indicate x-interceptIntercept at $(1; 0)$
  1 mark · Sketch an inverse graph
3. ✓
  Indicate additional pointe.g., $(3; - 1)$
  1 mark · Sketch an inverse graph
4. Question 6.3 · March 2023 · Provincial · 3 marks
The diagram shows the graph $f (x) = a^{x}$ . Point $B (3; 3 \frac{3}{8})$ lies on $f$ .
6.3 Draw the graph of $g$ , the reflection of $f$ in the line $y = x$ showing all the intercepts with the axes and the coordinates of another point on the graph.(3)
Show the memo (3 ticks)Memo
1. ✓
  Draw shapeLogarithmic shape increasing.
  1 mark · Sketch an inverse graph
2. ✓
  Indicate interceptx-intercept at $(1; 0)$ .
  1 mark · Sketch an inverse graph
3. ✓
  Indicate reflected pointPoint $(3 \frac{3}{8}; 3)$ or $(\frac{27}{8}; 3)$ .
  1 mark · Sketch an inverse graph
5. Question 5.4 · March 2023 · Provincial · 4 marks
The graph of $f (x) = \frac{2}{x + p} + q$ is sketched.
5.4 Draw a neat sketch of the graphs of $h$ and $h^{- 1}$ on the same set of axes. Clearly show all intercepts with axes, point of intersection and the axis of symmetry.(4)
Show the memo (4 ticks)Memo
1. ✓
  Sketch h(x)Line passing through y-intercept $(0; 8)$ and x-intercept $(- 4; 0)$ .
  1 mark · Draw a straight-line graph
2. ✓
  Sketch inverse h^(-1)(x)Line passing through y-intercept $(0; - 4)$ and x-intercept $(8; 0)$ .
  1 mark · Draw a straight-line graph
3. ✓
  Correct point of intersection $h$ and $h^{- 1}$ intersect at $(- 8; - 8)$
  1 mark · Sketch an inverse graph
4. ✓
  Axis of symmetry through the point of intersectionThe line $y = x$ (dashed) passes through $(- 8; - 8)$
  1 mark · Sketch an inverse graph
6. Question 4.2 · March 2025 · Provincial · 3 marks
The diagram below shows the graph of $k (x) = a^{x}$ . Point $B (3; 3 \frac{3}{8})$ lies on $k$ .
4.2 Draw the graph of $h$ , the reflection of $k$ in the line $y = x$ , showing all the intercepts with the axes and the coordinates of another point on the graph.(3)
Show the memo (3 ticks)Memo
1. ✓
  Draw shapeCorrect shape (logarithmic function shape)
  1 mark · Sketch an inverse graph
2. ✓
  Indicate x-interceptx-intercept at $(1; 0)$
  1 mark · Find the x-intercepts
3. ✓
  Indicate another pointPoint $(3 \frac{3}{8}; 3)$
  1 mark · Find the equation of an inverse

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