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

1MasterySAQ-SThe effect of transformations on the graph of a function6 marksPaper 2~9 min

The graph of

f(x) = x^2

is transformed to obtain the graph of

g(x) = (x-3)^2 + 2

(a)

State the two transformations that map the graph of

f

to the graph of

g

. [2 marks]

(b)

The point

P(2,\,4)

lies on the graph of

f

. Calculate the coordinates of the image of

P

on the graph of

g

. [2 marks]

(c)

A function

h

is obtained by applying the following two transformations to

f

in order: - translate by vector

\begin{pmatrix}-4\\0\end{pmatrix}

- then translate by vector

\begin{pmatrix}0\\5\end{pmatrix}

The graph of

h

is then reflected in the

y

-axis to give the graph of

k

. Determine the equation of

k

in the form

k(x) = (x+a)^2 + b

, where

a,b \in \mathbb{Z}

. [2 marks]

Solutions

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