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

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

The below shows the graph of

y = f(x)

for

-4 \leq x \leq 4

. The graph has a local maximum at

A(-2,\,5)

and a local minimum at

B(1,\,-3)

. The graph of

f

is transformed to obtain the graph of

g

, where

g(x) = 2f(x+1) - 3

(a)

Calculate the coordinates of the images of

A

and

B

on the graph of

g

. [4 marks]

(b)

The function

f

has a horizontal asymptote at

y = 0

. Write down the equation of the horizontal asymptote of

g

. [1 mark]

(c)

Determine the range of values of

x

for which

g(x) > 0

, given that

g

has exactly two zeros and that the zero with the larger

x

-value lies between the images of

A

and

B

found in part (a). Justify your answer. [1] Revised (c) — replacing trivial reflection with genuine AO3 discriminator: (c) The graph of

g

is further transformed by the mapping

(x,\,y) \mapsto (x,\,-y+k)

for some constant

k

. The image of

A'

under this combined transformation has the same

y

-coordinate as the image of

B'

. Find the value of

k

. [1] Final clean version: (a) Calculate the coordinates of the images of

A

and

B

on the graph of

g

. [4] (b) The function

f

has a horizontal asymptote at

y = 0

. Write down the equation of the horizontal asymptote of

g

. [1] (c) The graph of

g

is reflected in the

x

-axis to give the graph of

h

. The graph of

h

is then translated by

\begin{pmatrix}0\\k\end{pmatrix}

so that the image of

A'

and the image of

B'

have the same

y

-coordinate. Find the value of

k

. [1 mark]

Solutions

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