Grade 10 · CAPS

Grade 10 Functions and Graphs

Maths practice questions and a worked example

Grade 10 Functions and Graphs covers sketching, interpreting and finding the equations of linear, quadratic, hyperbolic and exponential functions — reading off domain, range, intercepts and asymptotes from a graph, and working out an unknown constant from a given point. Sourced from real November 2022-2023 Paper 1 questions where two graphs (e.g. a hyperbola and a straight line, or two parabolas) are sketched together and learners must find where they intersect or compare values.

Worked example

4.1.1 The sketch below shows the graphs of

f (x) = a^{x} - 3

and

g (x) = - \frac{4}{x} - 4

A (- 2; 6)

is a point on the graph of

f

and

B

is a point on the graph of

g

C

is the x-intercept of the graphs. Write down the domain of f.

Answer

x ∈ ℝ

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Functions and Graphs

Question 1 of 3

4.2 The function

p (x) = b^{x} + q

is described by the following properties:

b > 0; b \neq = 1

x

-intercept at

(2; 0)

, The horizontal asymptote is

y = - 9

4.2.1 Write down the range of

p

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Common mistakes

Reading the asymptote or intercept off the wrong axis, and confusing the domain restriction of a hyperbola (x ≠ 0 shifted) with its range restriction.

Grade 10 Functions and Graphs

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