#### Transcript of Gallery of Graphs

**Gallery of Graphs**

1. Rectangular Hyperbolas

2. Truncus

3.

4. Circles & Semi-Circles

5. Absolute Graphs

1) Rectangular Hyperbolas

2) Truncus

4) Circles

4) Semi-Circles

3)Graphs of the form

There are 5 types of Graphs you must recognise, draw and manipulate in this unit of work. They are:

All rectangular hyperbolas have this general shape. For the example given, there are 2

Asymptotes

. There is a

Vertical Asymptote at x=0

and a

Horizontal Asymptote at y=0

. Mark these in on your graph.

Transformations

There are 3 types of transformations associated with these graphs. They are:

*Dilations

*Reflections

*Translations

Complete Exercise 5A: All questions

Each graph must be labelled fully and include x/y intercepts and asymptotes (broken lines).

Always remember that to draw any graph, all you need to do is construct an appropriate table of values. However, you will save time if you can recognise the transformations as mentioned above.

A truncus shape is similar to the rectangular hyperbola with one exception. For x<0, the graph has been reflected in the x axis.

All Truncus Graphs have this general shape. For the example given, there are 2

Asymptotes

. There is a

Vertical Asymptote at x=0

and a

Horizontal Asymptote at y=0

. Mark these in on your graph.

Complete Exercise 5B: All questions

Each graph must be labelled fully and include x/y intercepts and asymptotes (broken lines).

Complete Exercise 5C: All questions

Each graph must be labelled fully and include x/y intercepts and the range and domain of each function.

c)

5) Absolute Graphs

Complete Exercise 5D: Questions 1,2,3(lhs), 4-8, 9(a,b,e)

Each graph must be labelled fully and include x/y intercepts.

The aim of this next exercise is to become familiar with this shape of graph and the effect of different transformations.

You should understand the effect of:

*dialtion (towards or away from the x-axis)

*translation, h units right, k units up

*reflection when 'a' is negative

*movement of asymptotes according to h & k

When transforming a graph, always do it in this order:

1) Dialations

2) Reflections

3) Translations

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