Grade 10 Maths · Trigonometry · Solve an inequality from a graph

Inequalities from Graphs Grade 10

Use a graph to find the x-values where it is above or below the x-axis or another graph (for example where f(x) > 0).

questions use it, all grades · 46 past paper, 61 practice: 107 questions use it, all grades · 46 past paper, 61 practice
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Question 7.2 · November 2024 · Paper 2 · National (DBE) · 2 marks

In the diagram below, the graph of

f (x) = tan x

is drawn for the interval

x \in [- 180°; 180°]

. $Diagram for this question$

7.2 Write down the values of

x

in the interval

x \in [- 180°; 0°]

for which

f (x) \leq 0

.(2)

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

More past paper questions: solve an inequality from a graph

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3. Question 5.3.1 · November 2025 · Paper 1 · National (DBE) · 2 marks
The graphs of $f (x) = a x^{2} + b x + c$ and $g (x) = \frac{- 4}{x - 3} + 8$ are drawn below.
P is the turning point of $f$ and the point of intersection of the asymptotes of $g$ .
The graphs intersect at $D (5; 6)$ . M and T are $x$ -intercepts of $f$ and $g$ respectively. $Diagram for this question$
5.3 Determine the values of $x$ for which:
5.3.1 $g (x) \leq f (x)$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Answer $3 < x \leq 5$ OR $x \in (3; 5]$
  2 marks · Solve an inequality from a graph
4. Question 6.4 · May/June 2024 · Paper 1 · National (DBE) · 2 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.
6.4 Write down the values of x for which $f (x) - g (x) > 0$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify interval left of first intersection $x < 0$
  1 mark · Solve an inequality from a graph
2. ✓
  Identify interval right of second intersection $x > 3$
  1 mark · Solve an inequality from a graph
5. Question 4.2.4 · May/June 2023 · Paper 1 · National (DBE) · 2 marks
4.2 Given: $f (x) = \frac{4}{x - 1} + 2$

Answer the questions that follow.
4.2.4 Use your graph to determine the values of $x$ for which $\frac{4}{x - 1} \geq - 2$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  $x \leq - 1$ $\frac{4}{x - 1} \geq - 2$
  $\frac{4}{x - 1} + 2 \geq 0$ , i.e. $f (x) \geq 0$
  
  $x \leq - 1$
  1 mark · Solve an inequality from a graph
2. ✓
  $x > 1$ $x > 1$
  1 mark · Solve an inequality from a graph
6. Question 6.5.1 · May/June 2023 · Paper 2 · National (DBE) · 2 marks
In the diagram below, the graph of $f (x) = tan (x - 45°)$ is drawn for $x \in [- 90°; 180°]$ . $Diagram for this question$
6.5 Use the graph(s) to determine the values of $x$ in the interval $x \in [- 90°; 90°]$ for which:
6.5.1 $f (x) > 1$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Answer $x \in (- 90°; - 45°)$ OR $- 90° < x < - 45°$
  2 marks · Solve an inequality from a graph

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