Transforming graphs: y = f(−x) | Maths | Quizalize & Oak National Academy

Starter quiz

$-\text{f}(x)$ transforms the graph of $\text{f}(x)$ by __________ $x$ -axis.

reflection in the ✓

rotation around the

translation from the

enlargement from the
Match each piece of function notation to a description.

$\text{f}(x)+1$

⇔

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

$\text{f}(x+1)$

⇔

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

$-\text{f}(x)$

⇔

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

$\text{f}(x)-1$

⇔

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

$\text{f}(x-1)$

⇔

The input has $1$ subtracted before the function is applied. ✓
The transformation of shape 'a' to shape 'b' could be described by __________.

rotation $90$ degrees clockwise around the origin

rotation $90$ degrees anti-clockwise around the origin

reflection in the $x$ -axis ✓

reflection in the $y$ -axis

translation by vector $\begin{pmatrix}0 \\ -10\end{pmatrix}$ ✓
The transformation of the point $(-3,2)$ to the position $(-3,-2)$ could be described by __________.

translation by vector $\begin{pmatrix}-4 \\ 0\end{pmatrix}$

translation by vector $\begin{pmatrix}0 \\ -4\end{pmatrix}$ ✓

reflection in the $x$ -axis ✓

reflection in the $y$ -axis

rotation $90$ degrees anti-clockwise around the origin
The point $(7,-9)$ is reflected in the $y$ -axis. What is its new position?

$(-9,7)$

$(9,-7)$

$(-7,-9)$ ✓

$(7,9)$

$(-7,9)$
The point $(-c,d)$ is reflected in the $y$ -axis. What is its new position?

$(d,-c)$

$(c,-d)$

$(-c,-d)$

$(c,d)$ ✓

Exit quiz

$\text{f}(-x)$ is a transformation by __________.

translation

rotation

reflection ✓

enlargement
$\text{f}(-x)$ is a transformation by reflection __________.

in the $y$ -axis ✓

in the line $y=x$

in the $x$ -axis

in the line $y=-x$
$y=\text{f}(x)$ is graphed. Which of these images shows the graph of $y=\text{f}(-x)$ ?
$Which point will remain invariant by the transformation <Math>y=\text{f}(-x)</Math>? Give your answer in the form <Math>(x,y)</Math> <span class="blank">______</span>$

Which point will remain invariant by the transformation $y=\text{f}(-x)$ ? Give your answer in the form $(x,y)$ ______

'(0, 1)' ✓
$Here is a table of values for an unknown function <Math>\text{f}(x)</Math>. Which coordinate pairs will be on the graph <Math>y=\text{f}(-x)</Math>?$

Here is a table of values for an unknown function $\text{f}(x)$ . Which coordinate pairs will be on the graph $y=\text{f}(-x)$ ?

$(-3,73)$

$(2,-24)$ ✓

$(1,-1)$

$(0,8)$ ✓

$(-1,3)$ ✓
$(e,f)$ 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 $y=\text{f}(-x)$ ?

$(-e,f)$ ✓

$(e,-f)$

$(e,f)$

$(-e,-f)$

Worksheet

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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 reflection in the y axis

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.

Keywords

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