Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
New
New
Year 11
Higher

Transforming graphs: y = f(−x)

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

Download all resources
arrow-right
Share activities with pupils
arrow-right
New
New
Year 11
Higher

Transforming graphs: y = f(−x)

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

Download all resources
arrow-right
Share activities with pupils
arrow-right
warning

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
arrow-right

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 is transformed by a reflection in the y axis

Keywords

  • Transformation - A transformation is a process that may change the size, orientation or position of a shape.

Common misconception

Pupils mix-up $$-$$f$$(x)$$ and f$$(-x)$$. Which is a reflection in the $$x$$-axis? Which is in the $$y$$-axis?

f$$(-x)$$ is the input being multiplied by $$-1$$ before the function is applied. Which coordinate is the input? The $$x$$ coordinates change from positive to negative so this must be a reflection in the $$y$$ axis.

Visually showing pupils f$$(-x)$$ using graphing technology demonstrates that it is a reflection in the $$y$$ axis. Showing pupils the comparison of two tables of values explains why this occurs.
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

Skip lesson video

Loading...

Starter quiz

Download starter quiz

6 Questions

Q1.
$$-\text{f}(x)$$ transforms the graph of $$\text{f}(x)$$ by __________ $$x$$-axis.
Correct answer: reflection in the
rotation around the
translation from the
enlargement from the
Q2.
Match each piece of function notation to a description.
Correct Answer:$$\text{f}(x)+1$$,The output of $$\text{f}(x)$$ has $$1$$ added to it.

The output of $$\text{f}(x)$$ has $$1$$ added to it.

Correct Answer:$$\text{f}(x+1)$$,The input has $$1$$ added to it before the function is applied.

The input has $$1$$ added to it before the function is applied.

Correct Answer:$$-\text{f}(x)$$,The output of $$\text{f}(x)$$ is multiplied by $$-1$$

The output of $$\text{f}(x)$$ is multiplied by $$-1$$

Correct Answer:$$\text{f}(x)-1$$,The output of $$\text{f}(x)$$ has $$1$$ subtracted from it.

The output of $$\text{f}(x)$$ has $$1$$ subtracted from it.

Correct Answer:$$\text{f}(x-1)$$,The input has $$1$$ subtracted before the function is applied.

The input has $$1$$ subtracted before the function is applied.

Q3.
The transformation of shape 'a' to shape 'b' could be described by __________.
An image in a quiz
rotation $$90$$ degrees clockwise around the origin
rotation $$90$$ degrees anti-clockwise around the origin
Correct answer: reflection in the $$x$$-axis
reflection in the $$y$$-axis
Correct answer: translation by vector $$\begin{pmatrix}0 \\ -10\end{pmatrix}$$
Q4.
The transformation of the point $$(-3,2)$$ to the position $$(-3,-2)$$ could be described by __________.
An image in a quiz
translation by vector $$\begin{pmatrix}-4 \\ 0\end{pmatrix}$$
Correct answer: translation by vector $$\begin{pmatrix}0 \\ -4\end{pmatrix}$$
Correct answer: reflection in the $$x$$-axis
reflection in the $$y$$-axis
rotation $$90$$ degrees anti-clockwise around the origin
Q5.
The point $$(7,-9)$$ is reflected in the $$y$$-axis. What is its new position?
$$(-9,7)$$
$$(9,-7)$$
Correct answer: $$(-7,-9)$$
$$(7,9)$$
$$(-7,9)$$
Q6.
The point $$(-c,d)$$ is reflected in the $$y$$-axis. What is its new position?
$$(d,-c)$$
$$(c,-d)$$
$$(-c,-d)$$
Correct answer: $$(c,d)$$

Exit quiz

Download exit quiz

6 Questions

Q1.
$$\text{f}(-x)$$ is a transformation by __________.
translation
rotation
Correct answer: reflection
enlargement
Q2.
$$\text{f}(-x)$$ is a transformation by reflection __________.
Correct answer: in the $$y$$-axis
in the line $$y=x$$
in the $$x$$-axis
in the line $$y=-x$$
Q3.
$$y=\text{f}(x)$$ is graphed. Which of these images shows the graph of $$y=\text{f}(-x)$$?
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q4.
Which point will remain invariant by the transformation $$y=\text{f}(-x)$$? Give your answer in the form $$(x,y)$$
An image in a quiz
Correct Answer: (0, 1), (0,1)
Q5.
Here is a table of values for an unknown function $$\text{f}(x)$$. Which coordinate pairs will be on the graph $$y=\text{f}(-x)$$?
An image in a quiz
$$(-3,73)$$
Correct answer: $$(2,-24)$$
$$(1,-1)$$
Correct answer: $$(0,8)$$
Correct answer: $$(-1,3)$$
Q6.
$$(e,f)$$ is on the graph of $$y=\text{f}(x)$$, $$e\neq{0}$$ and $$f\neq{0}$$. What will be the position of this point on the graph $$y=\text{f}(-x)$$?
Correct answer: $$(-e,f)$$
$$(e,-f)$$
$$(e,f)$$
$$(-e,-f)$$