Problem solving with graph transformations | Maths | Quizalize & Oak National Academy

Starter quiz

Match the transformed functions of $\text {f}(x)$ to their descriptions.

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

⇔

Translation of 5 in the positive $y$ direction ✓

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

⇔

Translation of 5 in the negative $x$ direction ✓

$\text {f}(5x)$

⇔

Stretch of $1 \over 5$ in the $x$ direction ✓

$5 \text {f}(x)$

⇔

Stretch of 5 in the $y$ direction ✓

$-\text {f}(x)$

⇔

Reflection in the $x$ axis ✓

$\text {f}(-x)$

⇔

Reflection in the $y$ axis ✓
$The graph of <Math>y= \text{f}(x)</Math> is labelled. What other function of <Math>x</Math> has been graphed?$

The graph of $y= \text{f}(x)$ is labelled. What other function of $x$ has been graphed?

$\text {f}(x + 2)$

$\text {f}(x - 2)$

$\text {f}(2x)$ ✓

$2\text {f}(x)$

$\text {f}\left({1\over2}x\right)$
$The graph of <Math>y= \text{f}(x)</Math> is labelled. What other function of <Math>x</Math> has been graphed?$

The graph of $y= \text{f}(x)$ is labelled. What other function of $x$ has been graphed?

$\text {f}(x + 2)$ ✓

$\text {f}(x - 2)$

$\text {f}(x) - 2$

$-\text {f}(x)$

$\text {f}(-x)$
$The graph of <Math>y= \text{g} (x)</Math> is labelled. What other function of <Math>x</Math> has been graphed?$

The graph of $y= \text{g} (x)$ is labelled. What other function of $x$ has been graphed?

$\text {g}(x) - 8$

$\text {g}(x- 8)$

$-\text {g}(x)$ ✓

$\text {g}(-x)$
An __________ is a line which a curve approaches but never touches.

asymptote ✓

axis

exponential

image

invariant line
Which of these is equivalent to $x^2 - 4x + 6$ ?

$(x-2)^2-4$

$(x-2)^2+2$ ✓

$(x-2)^2+10$

$(x-4)^2-10$

$(x-4)^2+6$

Exit quiz

The graph of $y=x^2$ has been transformed to get a new graph. What is the equation of this new graph?

$y=x^2 +3$

$y=x^2 -3$

$y=(x+3)^2$

$y=(x-3)^2$ ✓
The graph of $y=x^2$ has been transformed to get a new graph. What is the equation of this new graph?

$y=x^2 + 4x$ ✓

$y=x^2 - 4x$

$y=x^2 - 8x$

$y=x^2 + 4x + 8$

$y=x^2 + 4x - 8$
The graph of $y=x^2$ has been transformed to get a new graph. What is the equation of this new graph?

$y=-4x^2$ ✓

$y=-2x^2$

$y=2x^2$

$y=4x^2$
The graph of $y=x^2-2x$ has been transformed to get a new graph. What is the equation of this new graph?

$y=2x^2-2$

$y=2x^2+2$

$y=2x^2-4x+2$

$y=2x^2-8x+6$ ✓

$y=4x^2-8x+3$
$The graph of <Math>\text{f}(x)=2^x + 1</Math> has an asymptote at <Math>y=1</Math>. Match up the transformations with the equation of the asymptote after the transformation.$

The graph of $\text{f}(x)=2^x + 1$ has an asymptote at $y=1$ . Match up the transformations with the equation of the asymptote after the transformation.

$\text {f}(x+3)$

⇔

$y=1$ ✓

$\text {f}(x)+3$

⇔

$y=4$ ✓

$3\text {f}(x)$

⇔

$y=3$ ✓

$-\text {f}(x)$

⇔

$y=-1$ ✓
The graph of $\text{f}(x)= \text{tan}(x)$ where $-90 \le x \le 90$ has asymptotes at $x=-90$ and $x=90$ , which of these transformations will not change the position of the asymptotes ?

$-\text{f}(x)$ ✓

$3\text{f}(x)$ ✓

$\text{f}(x+30)$

$\text{f}(x) + 3$ ✓

$\text{f}(3x)$

Worksheet

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Lesson Details

Key learning points

Your knowledge of identifying transformations of shapes can be applied to graphs
This allows you to identify what transformations have taken place
Once the transformations have been identified, you can write this in function notation

Common misconception

Pupils may not see the link between transformations and manipulating algebraic expressions.

Be explicit in highlighting that the graph of $y=x^2+10x+22$ is the graph of $y=(x+5)^2-3$ which is the graph of $y=x^2$ transformed by the translation, \" $5$ units left, $3$ units down\".

Keywords

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