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

1MasterySAQ-STranslation, reflection, stretching and compression6 marksPaper 2~9 min

The function

f

is defined by

f(x) = x^2 - 4x + 7

for

x \in \mathbb{R}

. The graph of

f

is transformed by a translation of

\begin{pmatrix} 3 \\ -2 \end{pmatrix}

to give the graph of a function

g

(a)

Express

g(x)

in the form

(x - h)^2 + k

, where

h, k \in \mathbb{Z}

. [3 marks]

(b)

The graph of

g

is then reflected in the

x

-axis to give the graph of a function

p

. Write down

p(x)

in the form

-(x - h)^2 + k

. [1 mark]

(c)

Find the

x

-coordinates of the points where the graph of

p

intersects the graph of

f

. [2 marks]

Solutions

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