New
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.

New
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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Lesson details

Key learning points

  1. Desmos is an effective tool for showing the effects of this transformation
  2. The actual function itself does not need to be known
  3. 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.

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 (2024), 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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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:$$\text{f}(x)+11$$,The output of $$\text{f}(x)$$ has $$11$$ added to it.

The output of $$\text{f}(x)$$ has $$11$$ added to it.

Correct Answer:$$\text{f}(x+11)$$,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:$$11\text{f}(x)$$,The output of $$\text{f}(x)$$ is multiplied by $$11$$

The output of $$\text{f}(x)$$ is multiplied by $$11$$

Correct Answer:$$\text{f}(x)-11$$,The output of $$\text{f}(x)$$ has $$11$$ subtracted from it.

The output of $$\text{f}(x)$$ has $$11$$ subtracted from it.

Correct Answer:$$\text{f}(x-11)$$,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...
An image in a quiz
$$2$$ right, $$1$$ down.
Correct answer: $$4$$ right, $$6$$ down.
$$4$$ left, $$6$$ up.
vector $$\begin{pmatrix}4 \\ 6\end{pmatrix}$$
Correct answer: vector $$\begin{pmatrix}4 \\ -6\end{pmatrix}$$
Q4.
For the function $$\text{f}(x)$$, $$\text{f}(8)=37$$, match these transformations of the function to their values.
Correct Answer:$$\text{f}(8)+3$$,$$40$$

$$40$$

Correct Answer:$$3\text{f}(8)$$,$$111$$

$$111$$

Correct Answer:$$\text{f}(8)-3$$,$$34$$

$$34$$

Correct Answer:$$-3\text{f}(8)$$,$$-111$$

$$-111$$

Correct Answer:$$3\text{f}(8)-3$$,$$108$$

$$108$$

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: $$(-5,-a-4)$$
$$(-5,a-4)$$

6 Questions

Q1.
$$\text{f}(x)+a$$ is a transformation by...
reflection
rotation
Correct answer: translation
enlargement
Q2.
$$\text{f}(x)+a$$ translates the graph by $$a$$ in the...
Correct answer: $$y$$-direction
positive $$y$$-direction
$$x$$-direction
positive $$x$$-direction
Q3.
$$y=\text{f}(x)$$ is graphed here. The second line represents what transformation of $$y=\text{f}(x)$$?
An image in a quiz
Correct answer: $$y=\text{f}(x)+3$$
$$y=\text{f}(x)-3$$
$$y=\text{f}(x)+6$$
$$y=\text{f}(x)-6$$
Q4.
$$y=\text{f}(x)$$ is graphed here. Which coordinate pairs will be on the transformation $$y=\text{f}(x)-6$$?
An image in a quiz
$$(4,6)$$
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 $$\text{f}(x)$$. Which points will lie on the graph of $$y=\text{f}(x)+12$$?
$$(10,24)$$
Correct answer: $$(-2,36)$$
$$(12,8)$$
Correct answer: $$(0,20)$$
$$(-1,-13)$$
Q6.
$$(-c,d)$$ is on the graph of $$y=\text{f}(x)$$. What will the position of this point be if the graph is transformed by $$y=\text{f}(x)+a$$?
$$(a-c,d)$$
$$(-c,d-a)$$
Correct answer: $$(-c,d+a)$$
$$(c,a+d)$$