New

Year 11

Higher

Transforming graphs: y = f(x + a)

I can recognise the effect of applying the transformation y = f(x + a) to a graph.

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New

Year 11

Higher

Transforming graphs: y = f(x + a)

I can recognise the effect of applying the transformation y = f(x + a) to a graph.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson slides

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Lesson details

Key learning points

Desmos is an effective tool for showing the effects of this transformation
The actual function itself does not need to be known
The graph is transformed by a horizontal translation in the opposite direction

Keywords

Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
Transformation - A transformation is a process that may change the size, orientation or position of a shape or graph.

Common misconception

f $(x) + 5$ is a translation of $+ 5$ in the $y$ -direction so pupils may assume that f $(x + 5)$ is a translation of $+ 5$ in the $x$ -direction.

Visually showing pupils, using graphing technology, that f $(x + 5)$ is not a translation to the right will help. Showing them a comparison of the two tables of values for both functions shows them why this happens.

To help you plan your year 11 maths lesson on: Transforming graphs: y = f(x + a), download all teaching resources for free and adapt to suit your pupils' needs...

Using technology as a visual aid to model this transformation helps pupil to see that the curve of any graph remains congruent and the only change is it's position horizontally. Having access to Desmos.com and the ability to project it for pupils will support learning.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.

f (x) + a

is a of the graph of

f (x)

Correct Answer: transformation, translation

Q2.

Match each piece of function notation to a description.

Correct Answer:

f (x) + 4

,The output of

f (x)

has

4

added to it.

The output of $f (x)$ has $4$ added to it.

Correct Answer:

f (x + 4)

,The input has

4

added to it before the function is applied.

The input has $4$ added to it before the function is applied.

Correct Answer:

4 f (x)

,The output of

f (x)

is multiplied by

4

The output of $f (x)$ is multiplied by $4$

Correct Answer:

f (x) - 4

,The output of

f (x)

has

4

subtracted from it.

The output of $f (x)$ has $4$ subtracted from it.

Correct Answer:

f (x - 4)

,The input has

4

subtracted before the function is applied.

The input has $4$ subtracted before the function is applied.

Q3.

Shape 'a' has been transformed to shape 'b' by translation of __________.

3

right,

1

up.

Correct answer:

8

right,

3

up.

8

left,

3

down.

Correct answer: vector

(\begin{matrix} 8 \\ 3 \end{matrix})

vector

(\begin{matrix} 3 \\ 8 \end{matrix})

Q4.

The transformation of the point

(3, - 2)

to the position

(- 4, - 2)

could be described by __________.

translation by

7

in the positive

x

-direction.

Correct answer: translation by

7

in the negative

x

-direction.

translation by

7

in the negative

y

-direction.

Correct answer: translation by vector

(\begin{matrix} - 7 \\ 0 \end{matrix})

reflection in the line

x = - 1

Q5.

The point

(- 1, 13)

is translated

+ 8

in the

x

-direction. What is its new position?

Correct answer:

(7, 13)

(- 9, 13)

(- 1, 21)

(- 1, 5)

(8, 13)

Q6.

The point

(c, - d)

is translated by

9

in the negative

x

-direction. What is its new position?

(c, 9 - d)

(c, - d - 9)

(- 9, - d)

Correct answer:

(c - 9, - d)

(c + 9, - d)

Assessment exit quiz

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6 Questions

Q1.

f (x + a)

is a transformation by __________.

reflection

rotation

Correct answer: translation

enlargement

Q2.

f (x + a)

is a transformation by translation of __________.

a

in the

x

-direction.

Correct answer:

- a

in the

x

-direction.

a

in the

y

-direction.

- a

in the

y

-direction.

Q3.

y = f (x)

is graphed. Which of these images shows the transformation

y = f (x - 3)

Correct Answer: An image in a quiz

Q4.

y = f (x)

is graphed here. Which coordinate pairs will be on the transformation

y = f (x + 6)

(- 5, - 4)

Correct answer:

(- 11, - 10)

(4, - 1)

Correct answer:

(- 6, 5)

(0, - 1)

Q5.

y = f (x)

is graphed. What transformation can we see graphed?

y =

Correct Answer: f(x-7), y=f(x-7)

Q6.

y = f (x)

is graphed here. Which could the graph of the transformation be?

y = f (x + 45)

Correct answer:

y = f (x + 90)

y = f (x - 90)

Correct answer:

y = f (x - 270)

y = f (x + 270)

Transforming graphs: y = f(x + a)

Transforming graphs: y = f(x + a)

These resources will be removed by end of Summer Term 2025.

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Assessment exit quiz

6 Questions