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Transformations of Functions · Paper 2 — Free Maths AA HL Practice Questions

1MasterySAQ-STranslation, reflection, stretching, and compressions6 marksPaper 2~9 min

The function

f

is defined by

f(x) = x^2 + 4x + 3

, for

x \in \mathbb{R}

(a)

Write

f(x)

in the form

(x+h)^2 + k

, where

h, k \in \mathbb{Z}

. [2 marks]

(b)

The graph of

f

is transformed to the graph of

g

by a horizontal translation of

3

units to the left, followed by a vertical stretch with scale factor

2

about the

x

-axis. Find an expression for

g(x)

in the form

ax^2 + bx + c

, where

a, b, c \in \mathbb{Z}

. [3 marks]

(c)

Hence, write down the range of

g

. [1 mark]

Solutions

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