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

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.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

View new resources

Slide deck

Download slide deck

Skip slide deck

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 of the function is transformed by a vertical translation

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

Pupils may not see the vertical translation depending on the function used to show the effect of $a$ .

Ensure pupils consider a range of functions so that they can see the movement of the graph.

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 vertically. 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

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Starter quiz

Download starter quiz

6 Questions

Q1.

When every point of a shape moves the same distance in the same direction the transformation is called a...

Correct answer: translation

reflection

rotation

enlargement

Q2.

Match each piece of function notation to a description.

Correct Answer:

f (x) + 11

,The output of

f (x)

has

11

added to it.

The output of $f (x)$ has $11$ added to it.

Correct Answer:

f (x + 11)

,The input has

11

added to it before the function is applied.

The input has $11$ added to it before the function is applied.

Correct Answer:

11 f (x)

,The output of

f (x)

is multiplied by

11

The output of $f (x)$ is multiplied by $11$

Correct Answer:

f (x) - 11

,The output of

f (x)

has

11

subtracted from it.

The output of $f (x)$ has $11$ subtracted from it.

Correct Answer:

f (x - 11)

,The input has

11

subtracted before the function is applied.

The input has $11$ subtracted before the function is applied.

Q3.

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

2

right,

1

down.

Correct answer:

4

right,

6

down.

4

left,

6

up.

vector

(\begin{matrix} 4 \\ 6 \end{matrix})

Correct answer: vector

(\begin{matrix} 4 \\ - 6 \end{matrix})

Q4.

For the function

f (x)

f (8) = 37

, match these transformations of the function to their values.

Correct Answer:

f (8) + 3

40

$40$

Correct Answer:

3 f (8)

111

$111$

Correct Answer:

f (8) - 3

34

$34$

Correct Answer:

- 3 f (8)

- 111

$- 111$

Correct Answer:

3 f (8) - 3

108

$108$

Q5.

The point

(4, 1)

is translated 'up

5

'. What is it's new position?

Correct answer:

(4, 6)

(9, 6)

(4, 5)

(9, 1)

Q6.

The point

(- 5, - a)

is translated 'down

4

'. What is it's new position?

(- 1, - a)

(- 9, - a)

(- 5, - 4)

Correct answer:

(- 5, - a - 4)

(- 5, a - 4)

Exit quiz

Download exit quiz

6 Questions

Q1.

f (x) + a

is a transformation by...

reflection

rotation

Correct answer: translation

enlargement

Q2.

f (x) + a

translates the graph by

a

in the...

Correct answer:

y

-direction

positive

y

-direction

x

-direction

positive

x

-direction

Q3.

y = f (x)

is graphed here. The second line represents what transformation of

y = f (x)

Correct answer:

y = f (x) + 3

y = f (x) - 3

y = f (x) + 6

y = f (x) - 6

Q4.

y = f (x)

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

y = f (x) - 6

(4, 6)

Correct answer:

(4, - 6)

(- 6, 0)

Correct answer:

(0, - 6)

Correct answer:

(5, - 11)

Q5.

The points

(- 2, 24), (- 1, - 1), (0, 8)

lie on the graph of

f (x)

. Which points will lie on the graph of

y = f (x) + 12

(10, 24)

Correct answer:

(- 2, 36)

(12, 8)

Correct answer:

(0, 20)

(- 1, - 13)

Q6.

(- c, d)

is on the graph of

y = f (x)

. What will the position of this point be if the graph is transformed by

y = f (x) + a

(a - c, d)

(- c, d - a)

Correct answer:

(- c, d + a)

(c, a + d)

Transforming graphs: y = f(x) + a

Transforming graphs: y = f(x) + a

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

Slide deck

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Starter quiz

6 Questions

Exit quiz

6 Questions