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

Starter quiz

$\text{f}(x)+a$ and $\text{f}(x+a)$ transform the graph of $\text{f}(x)$ by __________.

addition

translation ✓

rotation

enlargement
Match each piece of function notation to a description.

$\text{f}(x)+5$

⇔

The output of $\text{f}(x)$ has $5$ added to it. ✓

$\text{f}(x+5)$

⇔

The input has $5$ added to it before the function is applied. ✓

$5\text{f}(x)$

⇔

The output of $\text{f}(x)$ is multiplied by $5$ ✓

$\text{f}(x)-5$

⇔

The output of $\text{f}(x)$ has $5$ subtracted from it. ✓

$\text{f}(x-5)$

⇔

The input has $5$ subtracted before the function is applied. ✓
The transformation of the point $(3,4)$ to the position $(-3,4)$ could be described by __________.

translation by $6$ to the left ✓

translation by vector $\begin{pmatrix}-6 \\ 0\end{pmatrix}$ ✓

translation by vector $\begin{pmatrix}0 \\ -6\end{pmatrix}$

reflection in the $x$ -axis

reflection in the $y$ -axis ✓
The transformation of the point $(-2,5)$ to the position $(-2,-5)$ could be described by __________.

Translation by vector $\begin{pmatrix}-10 \\ 0\end{pmatrix}$

Translation by vector $\begin{pmatrix}0 \\ 10\end{pmatrix}$

Translation by vector $\begin{pmatrix}0 \\ -10\end{pmatrix}$ ✓

reflection in the $x$ -axis ✓

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

$(-7,-9)$

$(-7,9)$

$(-9,7)$

$(7,9)$ ✓
The point $(-a,b)$ is reflected in the $x$ -axis. What is its new position?

$(b,-a)$

$(-a,-b)$ ✓

$(a,-b)$

$(a,b)$

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 $y=-x$
$<Math>y=\text{f}(x)</Math> is graphed here. Which coordinate pairs will be on the transformed graph <Math>y=-\text{f}(x)</Math>?$

$y=\text{f}(x)$ is graphed here. Which coordinate pairs will be on the transformed graph $y=-\text{f}(x)$ ?

$(0,6)$

$(-6,0)$

$(1,-3)$ ✓

$(2,-2)$ ✓

$(-2,-2)$
$y=\text{f}(x)$ is graphed. Which of these images shows the transformation $y=-\text{f}(x)$ ?
$Here is a table of values for an unknown function <Math>\text{f}(x)</Math> Which coordinate pairs will be on the transformed graph <Math>y=-\text{f}(x)</Math>?$

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

$(3,-111)$

$(3,111)$

$(-2,40)$ ✓

$(0,-24)$ ✓

$(-1,-29)$
$(-c,-d)$ is on the graph of $y=\text{f}(x)$ , $c\neq{0}$ and $d\neq{0}$ . What will be the position of this point on the graph $y=-\text{f}(x)$ ?

$(-c,-d)$

$(c,-d)$

$(-c,d)$ ✓

$(c,d)$

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

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 x axis

Common misconception

Pupils can get confused between $-$ f $(x)$ and f $(-x)$ , which one is a reflection in the $x$ -axis and which is a reflection in the $y$ -axis?

Interpreting the notation is key. Remind pupils that $-$ f $(x)$ is the output of f $(x)$ being multiplied by $-1$ . Which coordinate is the output? The $y$ coordinates are altered from positive to negative, that is a reflection in which axis?

Keywords

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