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Transformations of Functions · Paper 1 — Free Maths AA SL Practice Questions

1FoundationSAQ-STranslation, reflection, stretching, and compressions5 marksPaper 1~8 min

The function

f

is defined by

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

(a)

Write down the coordinates of the vertex of the graph of

f

. [1 mark]

(b)

The graph of

f

is stretched vertically by a scale factor of

2

about the

x

-axis. Write down the vertex form of the resulting function. [2 marks]

(c)

The graph from part (b) is then translated

1

unit to the right. Find the equation of the resulting function

g

, giving your answer in the form

g(x) = a(x-h)^2 + k

. [2 marks]

Solutions

2FoundationSAQ-STranslation, reflection, stretching, and compressions4 marksPaper 1~6 min

The graph of

y = f(x)

consists of two straight line segments: from

(-4,\,0)

(0,\,4)

, and from

(0,\,4)

(4,\,0)

. The function

g

is obtained by translating

f

2

units to the left and

1

unit down.

(a)

Write down the coordinates of the vertex of

g

. [1 mark]

(b)

Find the equation of the right-hand line segment of

g

in the form

y = mx + c

. [3 marks]

Solutions

3MasterySAQ-STranslation, reflection, stretching, and compressions5 marksPaper 1~8 min

The function

f

is defined by

f(x) = x^2 + 4x + 5

, for

x \in \mathbb{R}

(a)

The graph of

f

is translated by the vector

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

to give the graph of a function

g

. Show that

g(x) = x^2 - 2x - 1

. [2 marks]

(b)

The graph of

g

is then reflected in the

y

-axis to give the graph of a function

h

. Find an expression for

h(x)

in the form

h(x) = ax^2 + bx + c

. [3 marks]

Solutions

4ChallengeSAQ-LTranslation, reflection, stretching, and compressions8 marksPaper 1~12 min

The function

f

is defined by

f(x) = x^2

, for

x \in \mathbb{R}

. The graph of

f

undergoes the following transformations in sequence: 1. A horizontal stretch by scale factor

\frac{1}{2}

2. A translation by the vector

\begin{pmatrix} 1 \\ -3 \end{pmatrix}

3. A reflection in the

x

-axis Let

g

be the resulting function.

(a)

Determine an expression for

g(x)

in the form

a(x-h)^2 + k

, where

a, h, k \in \mathbb{R}

. [4 marks]

(b)

The graphs of

g

and

f

intersect at two points. Determine the

x

-coordinates of these points and hence find the exact area of the region enclosed between the two graphs. [4 marks]

Solutions

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