Skip to content
###### A-Level H2 Math | 5 Essential Questions

# Transformations of Graphs

*This free online revision course is specially designed for students to revise important topics from A Level H2 Maths. The course content is presented in an easy to study format with 5 essential questions, core concepts and explanation videos for each topic. Please download the worksheet and try the questions yourself! Have fun learning with us, consider joining our tuition classes or online courses.*

##### 2021 NJC Lecture Test (b)

**Suggested Handwritten and Video Solutions**

##### ACJC Tutorial 3 Q9

**Suggested Handwritten and Video Solutions**

##### 2013 VJC P1 Q6 (i)

**Suggested Handwritten and Video Solutions**

**2020 VJC Promo Q8**

**Suggested Handwritten and Video Solutions**

**2019 RI P1 Q5**

**Suggested Handwritten and Video Solutions**

Transformation, in mathematics, is a change in the form of a mathematical object without changing the underlying properties of that object. We can perform a transformation on an object by moving it from one place to another on the coordinate plane according to some rules. There are four types of transformations, namely translation, reflection, dilation, and rotation.

- Q1
- Q2
- Q3
- Q4
- Q5

The diagram below shows a sketch of the curve with equation $y=\text{g}(x)$. The curve has asymptotes with equations$x=0$ and $y=2$. The curve crosses the $x$-axis at $A(2,0)$ and $C(7,0)$ and has a turning point at $B(4,-2)$.

On separate diagrams, sketch the curves with equations

(i)

$y=\left| \text{g}(-x) \right|$,

[3]

(i) $y=\left| \text{g}(-x) \right|$,

[3]

(ii)

$y=\frac{1}{\text{g}(x)}$.

[4]

(ii) $y=\frac{1}{\text{g}(x)}$.

[4]

For each curve, state clearly the equations of any asymptotes, the coordinates of any turning points and the coordinates of any points where the curves crosses the $x$- and $y$- axes.

- (i)
- (ii)

- (i)
- (ii)

**Share with your friends!**

WhatsApp

Telegram

Facebook

A graph with the equation $y=\text{f}(x)$ undergoes, in succession, the following transformations:

$B$: A stretch parallel to the $x$- axis by factor $\frac{1}{2}$.

$C$: A reflection in the $y$- axis.

The equation of the resulting curve is $y=\frac{2}{2{{x}^{2}}+2x+1}$. Determine the equation $y=\text{f}(x)$.

**Share with your friends!**

WhatsApp

Telegram

Facebook

The diagram shows the graph of $y=\text{f}(x)$ which has a minimum point at $(0, 2)$ and asymptotes $x=2$ and $y=5.$

On separate diagrams, sketch the graphs of $y\ =\ \ \frac{1}{\text{f}(x)}$.

**Share with your friends!**

WhatsApp

Telegram

Facebook

(a)

The graph of $y=\text{f}(x)$ is shown in the diagram. It passes through the origin and has a minimum point at $\left( 2,\text{ }0 \right)$. The lines $x=1$ and $y=2$ are the asymptotes of the graph.Sketch the graph of $y=2-\text{f}(x)$, stating the coordinates of the point where the graph crosses the $y$-axis, the coordinates of any stationary point(s) and the equations of any asymptotes.

[2]

(a) The graph of $y=\text{f}(x)$ is shown in the diagram. It passes through the origin and has a minimum point at $\left( 2,\text{ }0 \right)$. The lines $x=1$ and $y=2$ are the asymptotes of the graph.Sketch the graph of $y=2-\text{f}(x)$, stating the coordinates of the point where the graph crosses the $y$-axis, the coordinates of any stationary point(s) and the equations of any asymptotes.

[2]

(b)

The curve $C$ has equation $y=\frac{2{{x}^{2}}+kx-2}{x+2}$, where $k$ is a constant.

(b) The curve $C$ has equation $y=\frac{2{{x}^{2}}+kx-2}{x+2}$, where $k$ is a constant.

(i)

Find the set of values of $k$ for which $C$ has $2$ stationary points.

[3]

(i) Find the set of values of $k$ for which $C$ has $2$ stationary points.

[3]

For the rest of the question, take $k=-3$.

For the rest of the question, take $k=-3$.

(ii)

By expressing the equation $y=\frac{2{{x}^{2}}-3x-2}{x+2}$ in the form $y=ax+b+\frac{c}{x+2}$, where $a$, $b$ and $c$ are constants, write down the equations of the asymptotes of $C$.

[3]

(ii) By expressing the equation $y=\frac{2{{x}^{2}}-3x-2}{x+2}$ in the form $y=ax+b+\frac{c}{x+2}$, where $a$, $b$ and $c$ are constants, write down the equations of the asymptotes of $C$.

[3]

(iii)

Hence sketch $C$, giving the equations of any asymptotes, the coordinates of any stationary points and of the points where $C$ crosses the axes.

[2]

(iii) Hence sketch $C$, giving the equations of any asymptotes, the coordinates of any stationary points and of the points where $C$ crosses the axes.

[2]

(iv)

Describe a pair of transformations which transform the graph of $y=x+\frac{6}{x+2}$ to $C$.

[2]

(iv) Describe a pair of transformations which transform the graph of $y=x+\frac{6}{x+2}$ to $C$.

[2]

- (a)
- (b)(i)
- (b)(ii)
- (b)(iii)
- (b)(iv)

- (a)
- (b)(i)
- (b)(ii)
- (b)(iii)
- (b)(iv)

**Share with your friends!**

WhatsApp

Telegram

Facebook

The diagram shows the graph of Folium of Descartes with cartesian equation

${{x}^{3}}+{{y}^{3}}=3axy$,

where a is a positive constant. The curve passes through the origin, and has an oblique asymptote with equation $y=-x-a$.

(i)

Given that $\left( 0,0 \right)$ is a stationary point on the curve, find, in terms of a, the coordinates of the other stationary point.

[5]

(i) Given that $\left( 0,0 \right)$ is a stationary point on the curve, find, in terms of a, the coordinates of the other stationary point.

[5]

(ii)

Sketch the graph of

${{\left| x \right|}^{3}}+{{y}^{3}}=3a\left| x \right|y$,

including the equations of any asymptotes, coordinates of the stationary points and the point where the graph crosses the $x$-axis.

[3]

(ii) Sketch the graph of

${{\left| x \right|}^{3}}+{{y}^{3}}=3a\left| x \right|y$,

including the equations of any asymptotes, coordinates of the stationary points and the point where the graph crosses the $x$-axis.

[3]

- (i)
- (ii)

- (i)
- (ii)

**Share with your friends!**

WhatsApp

Telegram

Facebook

**Download Transformations of Graphs Worksheet**

**Learn more about our H2 Math Tuition**

Play Video

**H2 Math Question Bank**

Check out our question bank, where our students have access to thousands of H2 Math questions with video and handwritten solutions.

**Share with your friends!**

WhatsApp

Telegram

Facebook

How can we help?

Pure Math

Statistics