You're viewing 1 free preview question for Maths AA HL — subscribe to unlock 7 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Transformations of Functions · Paper 3 — Free Maths AA HL Practice Questions

1ChallengeLAQTranslation, reflection, stretching, and compressions10 marksPaper 3~15 min

Data

1. A horizontal stretch by scale factor

\dfrac{1}{2}

(compression towards the

y

-axis). 2. A reflection in the

y

-axis. 3. A translation by

\begin{pmatrix} 3 \\ 0 \end{pmatrix}

Consider

f(x) = \ln(x)

for

x > 0

. Let

g(x)

be obtained by applying the following transformations to

f(x)

in the order

(a)

Show that

g(x) = \ln(-2x + 6)

, and state the domain of

g

. [4 marks]

(b)

Using the log identity

\ln(ab) = \ln a + \ln b

, express

g(x)

in the form

A + \ln(B - x)

, where

A

and

B

are exact constants to be found. [2 marks]

(c)

A student claims that applying the three transformations in the order: translate → horizontal stretch → reflect produces the same function

g(x)

. Determine the function

g_{\text{new}}(x)

produced by this reordering, state its domain, and hence evaluate whether the student's claim is correct, justifying your answer by comparing

g_{\text{new}}(x)

with

g(x)

from part (b). [4 marks]

Solutions

Questions 2-8

Unlock these questions with Premium

That's every free question here — 1 of 8.

+7 more questions, plus Mock Papers & Worksheets, are waiting in Premium.