Composite Functions

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Composite Functions — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionInterpret compositeConcept Practice

2 marks~3 minCriterion A

A security camera at position

P = (2, 3)

on a coordinate grid (units in metres) undergoes a composite transformation: a rotation of

90°

clockwise about the origin, followed by a reflection across the

y

-axis.

Determine the final coordinates of the camera's image

P''

after both transformations. [1]

The camera has a maximum effective range of 3.5 m from the origin. Justify whether the composite transformation places the camera within its effective range. [1]

Solutions

2Questionf(g(x)) conceptAssessment Practice

2 marks~3 minCriterion D

A clothing store applies a 10% discount followed by an 8% sales tax on all items. Let

x

be the original price in dollars, where

f(x) = 0.9x

represents the discount and

g(x) = 1.08x

represents the tax.

Determine

g(f(x))

and

f(g(x))

, and hence advise the store manager which order of operations to advertise to best serve customer perception. [2]

Solutions

3QuestionEvaluate compositeAssessment Practice

4 marks~6 minCriterion C

The graphs of two functions,

f(x)

and

g(x)

, are shown below.

[Imagine two graphs are shown: one for

f(x)

and one for

g(x)

.

The graph of $f(x)$ is a straight line passing through the points $(0, 1)$ and $(2, 5)$ .
The graph of

g(x)

is a curve passing through the points

(1, 3)

and

(5, 7)

.]

Explain how you would determine the value of

g(f(2))

using these graphs. In your explanation, clearly show the order of operations and state the values you read from each graph at each step. Use complete sentences and proper mathematical notation.

Solutions

4QuestionInterpret compositeAssessment Practice

6 marks~9 minCriterion B

A factory uses two automated processes to price its products. Process

f

converts a raw material quantity

x

(kg) into a base unit count:

f(x) = 2x + 1

. Process

g

then converts the base unit count into a final price (dollars).

x

: 1, 2, 3, 4 —

f(x)

: 3, 5, 7, 9

x

: 3, 5, 7, 9 —

g(x)

: 9, 15, 21, 27

Calculate

g(f(2))

and

g(f(3))

using the tables above. [2]

Deduce an algebraic expression for

g(x)

. [2]

A bulk order requires 10 kg of raw material. The factory's budget allows a maximum spend of 60 dollars. Advise the factory manager whether the order should proceed, justifying your answer using

g(f(10))

. [2]

Solutions

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