Grade 10 Maths · Functions

Sketch a graph from its equation

Draw a parabola, hyperbola, exponential or cubic graph from its equation with the right shape, direction and position, showing key points.

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Parabola Grade 10: How to drawKevinmathscience

How to Draw a Hyperbola: Grade 10 FunctionsMiss Martins Maths and Science

Exponential Function Grade 10: How to drawKevinmathscience

Draw Cubic Graph Grade 12Kevinmathscience

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Question 4.3 · November 2024 · Paper 1 · National (DBE) · 3 marks

Given:

f (x) = a^{x} - 1

for

a > 0

B (2; \frac{- 5}{9})

is a point on

f

4.3 Sketch the graph of

f

. Clearly show the intercepts with the axes and asymptotes, if any.(3)

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

More past paper questions: sketch a graph from its equation

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

3. Question 4.1.1 · June 2025 · Paper 1 · Provincial · 3 marks
4.1 Given: $f (x) = - x^{2} + 4$
4.1.1 Sketch the graph of $f$ . Clearly indicate all the intercepts with the axes on the graph.(3)
Show the memo (1 tick)Memo
1. ✓
  Describe the correct sketch of the graphThe graph must be a parabola showing:
  1. A concave down shape (opening downwards)
  2. A y-intercept and turning point at $(0; 4)$
  3. Two x-intercepts at $(- 2; 0)$ and $(2; 0)$
  3 marks · Sketch a graph from its equation
4. Question 9.4 · May/June 2025 · Paper 1 · National (DBE) · 4 marks
Given: $f (x) = x^{3} - 6 x^{2} + 9 x - 4 = (x - 4) (x - k)^{2}$
9.4 Draw the graph of $f$ . Label ALL turning points and intercepts with the axes.(4)
Show the memo (4 ticks)Memo
1. ✓
  Plot the turning pointsTurning points at $(1; 0)$ and $(3; - 4)$ are indicated.
  1 mark · Find stationary points
2. ✓
  Plot the x-interceptsThe roots of $f (x) = (x - 4) (x - 1)^{2}$ are $x = 4$ and $x = 1$ .
  x-intercepts at $(1; 0)$ and $(4; 0)$ are indicated.
  1 mark · Find the x-intercepts
3. ✓
  Plot the y-interceptEvaluate $f (0) = - 4$ .
  y-intercept at $(0; - 4)$ is indicated.
  1 mark · Find the y-intercept
4. ✓
  Draw the overall shape of the cubic graphGraph starts in the third quadrant, goes up to local max at $(1; 0)$ , down to local min at $(3; - 4)$ , and up through $(4; 0)$ into the first quadrant.
  1 mark · Sketch a graph from its equation
5. Question 4.2 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
Given: $g (x) = \frac{1}{x - 1} + 2$
4.2 Draw a graph of $g$ , indicating any intercepts with the axes and asymptotes.(4)
Show the memo (4 ticks)Memo
1. ✓
  Identify hyperbola shape in correct quadrantsCorrect shape
  1 mark · Sketch a graph from its equation
2. ✓
  Indicate dashed asymptotes $x = 1, y = 2$
  1 mark · State the asymptotes
3. ✓
  Mark x-intercept0,5
  1 mark · Find the x-intercepts
4. ✓
  Mark y-intercept1
  1 mark · Find the y-intercept
6. Question 6.4 · June 2024 · Paper 1 · Provincial · 4 marks
Given: $k (x) = \frac{- 4}{x + 3} + 1$ and $h (x) = 2^{- x} - 4$
6.4 Sketch the graph of k and h on the same axes. Clearly indicate ALL intercepts with the axes as well as the asymptotes.(4)
Show the memo (4 ticks)Memo
1. ✓
  Shape of k $k (x) = \frac{- 4}{x + 3} + 1$ : hyperbola with $a < 0$ , its branches in the 2nd and 4th quadrants formed by the asymptotes
  1 mark · Sketch a graph from its equation
2. ✓
  k and h intercepts $k$ : $(1; 0)$ and $(0; - \frac{1}{3})$
  $h$ : $(- 2; 0)$ and $(0; - 3)$
  1 mark · Find the x-intercepts
3. ✓
  Asymptotes of k and h $k$ : $x = - 3$ and $y = 1$
  $h$ : $y = - 4$
  1 mark · State the asymptotes
4. ✓
  Shape of h $h (x) = 2^{- x} - 4$ : decreasing exponential graph approaching $y = - 4$ on the right
  1 mark · Sketch a graph from its equation

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