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VCE 12 Methods 2023

2.03 Piecewise-defined and composite functions

Interactive practice questions

Use the graph of $g$g to solve the following:

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a

Find $g\left(-4\right)$g(4).

b

Find $g\left(2\right)$g(2).

c

Find $g\left(-10\right)$g(10).

d

Find $x$x when $g\left(x\right)=-1$g(x)=1.

Easy
1min

Use the graph of $f\left(x\right)$f(x) to answer the following. Where applicable, use interval notation:

Easy
4min

Consider the function below:

Easy
2min

Consider the function:

Easy
5min
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Outcomes

U34.AoS1.10

the concepts of domain, maximal domain, range and asymptotic behaviour of functions

U34.AoS1.5

graphs of sum, difference, product and composite functions involving functions of the types specified above (not including composite functions that result in reciprocal or quotient functions)

U34.AoS1.12

the concept of combined functions, and the connection between domain and range of the functions involved and the domain and range of the combined functions

U34.AoS1.17

find the rule of a composite function and give its domain and range

U34.AoS2.3

composition of functions, where f composite 𝑔, 𝑓 ∘ 𝑔, is defined by (𝑓 ∘ 𝑔)(𝑥) = 𝑓(g(x)

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