Grade 10 Maths · Functions

State the domain and range

Write the x-values a graph covers (domain) and the y-values it reaches (range) (for example y = x² + 1 has range y ≥ 1).

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Exponential Domain Range| Grade 11 FunctionsKevinmathscience

Domain and Range of a Parabola (Grade 10,11 and 12 Mathematics)MatheNatic

Domain and Range for Functions: Grade 10 MathsMiss Martins Maths and Science

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Question 6.2 · November 2024 · Paper 1 · Provincial · 2 marks

The graphs of

f (x) = \frac{4}{x} - 2

and

g (x) = m x + c

are drawn below. A(4; 4), B, D(0; -4) and E are points on g. B is the x-intercept of both f and g. B and E are the points of intersection of f and g. AC is parallel to the y-axis, with C a point on f. Diagram for this question

6.2 Write down the range of f.(2)

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

More past paper questions: state the domain and range

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3. Question 6.4 · November 2023 · Paper 1 · Provincial · 2 marks
Given: $f (x) = 2 (3^{x}) + 1$
6.4 Write down the range of $h$ , if $h (x) = 2 (3^{x + 1}) - 5$ .(2)
Show the memo (1 tick)Memo
1. ✓
  Answer $y > - 5$
  2 marks · State the domain and range
4. Question 5.5 · November 2024 · Paper 1 · Provincial · 3 marks
The lines $y = - x + 4$ and $y = x - 2$ are the axes of symmetry of the function $f (x) = \frac{- 3}{x + p} + q$ .
5.5 Write down the domain of $g$ if $g$ is the reflection of $f$ along the line $x = 0$ .(3)
Show the memo (2 ticks)Memo
1. ✓
  Vertical asymptoteVertical asymptote of $g$ (by inspection): $x = - 3$
  
  OR: $g (x) = f (- x) = \frac{- 3}{- x - 3} + 1$ ; $- x - 3 = 0$ ; $x = - 3$
  1 mark · Reflect a graph
2. ✓
  Domain $∴ x \in R; x \neq = - 3$
  2 marks · State the domain and range
5. Question 5.4 · November 2025 · Paper 1 · Provincial · 3 marks
The graphs of $f (x) = \frac{a}{x + p} + q$ and $g (x) = \frac{x}{3} + c$ are drawn below. C $(3; - 1)$ is the point of intersection between the asymptotes of $f$ . A and B are $x$ - and $y$ -intercepts of $f$ and $g$ respectively. E $(4; 2)$ is a point on $f$ in the first quadrant. $Diagram for this question$
5.4 Write down the domain of $h$ , if $h (x) = f [- (x - 4)]$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Replacing $x$ by $- (x - 4)$ Vertical asymptote of $f$ : $x - 3 = 0$ , so for $h$ :
  $- (x - 4) - 3 = 0$
  1 mark · Shift or reflect a graph
2. ✓
  $x - 1 = 0$ / $x = 1$ $- x + 4 - 3 = 0$
  $- x + 1 = 0$
  $x - 1 = 0$
  V.A.: $x = 1$
  1 mark · State the asymptotes
3. ✓
  AnswerDomain: $x \in R$ ; $x \neq = 1$
  1 mark · State the domain and range
6. Question 6.2 · May/June 2025 · Paper 1 · National (DBE) · 1 mark
The graphs of $f (x) = p^{x} + q$ and $g (x) = m x + c$ are drawn below. $A (3; 4)$ is the point of intersection of $f$ and $g$ . $B (0; - 3)$ is the y-intercept of $f$ . E is the x-intercept of $g$ .
6.2 Write down the range of $f$ .(1)
Show the memo (1 tick)Memo
1. ✓
  Identify horizontal asymptoteThe asymptote is $y = q = - 4$ . The graph sits above the asymptote.
  Range: $y > - 4$ OR $y \in (- 4; \infty)$
  1 mark · State the domain and range

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