Grade 10 Maths · Trigonometry · State increasing and decreasing intervals

Increasing and Decreasing Functions Grade 10

Give the x-values where a graph is going up or going down (for example y = x^2 is decreasing for x < 0 and increasing for x > 0).

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Question 9.1 · November 2024 · Paper 1 · National (DBE) · 2 marks

A (1; 9)

and

B (\frac{5}{2}; 8)

are the turning points of graph

f

below.

C (0; 7)

is the y-intercept of

f

9.1 For which values of

x

f

decreasing?(2)

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

More past paper questions: state increasing and decreasing intervals

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3. Question 8.5.1 · May/June 2023 · Paper 1 · National (DBE) · 2 marks
Given: $f (x) = x^{3} + 4 x^{2} - 7 x - 10$
8.5 Use your graph to determine the values of $x$ for which:
8.5.1 $f^{'} (x) < 0$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Answer $x \in (- 3, 4; 0, 7)$ OR $- 3, 4 < x < 0, 7$
  2 marks · State increasing and decreasing intervals
4. Question 9.3.2 · May/June 2022 · Paper 1 · National (DBE) · 2 marks
Sketched below is the graph of $f (x) = x^{3} + a x^{2} + b x + c$ .
The $x$ -intercepts of $f$ are at $(3; 0)$ and M, where M lies on the negative $x$ -axis.

$K (0; - 3)$ is the $y$ -intercept of $f$ .
M and N are the turning points of $f$ . $Diagram for this question$
9.3 For which values of $x$ will:
9.3.2 $f$ be increasing(2)
Show the memo (2 ticks)Memo
1. ✓
  $x < - 1$ $x < - 1$
  1 mark · State increasing and decreasing intervals
2. ✓
  $x > \frac{5}{3}$ $x < - 1$ or $x > \frac{5}{3}$
  1 mark · State increasing and decreasing intervals
5. Question 7.4.2 · May/June 2022 · Paper 2 · National (DBE) · 2 marks
In the diagram below, the graphs of $f (x) = \frac{1}{2} cos x$ and $g (x) = sin (x - 3 0^{\circ})$ are drawn for the interval $x \in [- 9 0^{\circ}; 24 0^{\circ}]$ . A and B are the $y$ -intercepts of $f$ and $g$ respectively. $Diagram for this question$
7.4 For which values of $x$ , in the interval $x \in [- 9 0^{\circ}; 24 0^{\circ}]$ , will:
7.4.2 $g^{'} (x - 5^{\circ}) > 0$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Critical values $g$ increases from $- 6 0^{\circ}$ to $12 0^{\circ}$ ; shifted $5^{\circ}$ right: $- 5 5^{\circ}$ and $12 5^{\circ}$
  1 mark · Shift a graph
2. ✓
  Answer $x \in (- 5 5^{\circ}; 12 5^{\circ})$ OR $- 5 5^{\circ} < x < 12 5^{\circ}$
  1 mark · State increasing and decreasing intervals
6. Question 5.4.1 · September 2026 · Paper 1 · Provincial · 2 marks
The graphs of $f (x) = a (x + p)^{2} + q$ for $x \geq - 4$ and $g (x) = m x + c$ are sketched below.

• Points A and B are the $x$ -intercepts of $f$ .
• C(1 ; 18) is the turning point of $f$ .
• D(0 ; 16) is a point of intersection of $f$ and $g$ . $Diagram for this question$
5.4 For which value(s) of $x$ is:
5.4.1 $f$ increasing?(2)
Show the memo (2 ticks)Memo
1. ✓
  Answer $- 4 \leq x < 1$ OR $x \in [- 4; 1)$
  2 marks · State increasing and decreasing intervals

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