# TRANSFORMATIONS OF FUNCTIONS

## About the topic "Transformations of functions"

"Transformations of functions" is the stuff which is much required for the students who study math  in  both school level and college level.

Even though students can get this stuff on internet, they do not understand exactly what has been explained.

To make the students to understand the stuff "Transformations", we have explained each kind of transformation  step by step explanation along with the corresponding figures.

## Transformations - Definition

A very simple definition for transformations is, whenever a figure is moved from one location to another location, a Transformation occurs.

If a figure is moved from one location another location, we say, it is transformation. Our next question is, how will the transformation be?. To know that, we have to be knowing the different types of transformations.

Now, let us come to know the different types of transformations.

## Different types of "Transformations of functions"

The different types of transformations which we can do in the functions are

1. Horizontal Translation

2. Vertical Translation

3. Reflection through the x-axis

4. Reflection through the y-axis

6. Vertical Expansions and Compressions

## What is "Image" and "Pre-image"?

When a transformation occurs, the original figure is known as the pre-image and the new figure is known as the image.

It has been clearly shown in the below picture.

When a figure is moved from one location to another location, we say that it is a transformation.

In this point, always students have a question.

That is, if a figure is moved from one location to another location, we say, "it is transformation". How is this transformation made?

More clearly, on what grounds is the transformation made?

Is there any pre-decided rule to make transformation?

Yes, there is a pre-decided rule to make each and every transformation.

The rule we apply to make transformation is depending upon the kind of transformation we make.

We have already seen the different types of transformations in functions.

For example, if we are going to make transformation of a function using reflection through the x-axis, there is a pre-decided rule for that. According to the rule, we have to make transformation.

The rule that we apply to make transformation using reflection and the rule we apply to make transformation using rotation are not same.

Hence, for each type of transformation, we may have to apply different rule.

After having gone through the stuff given above, we hope that the students would have understood "Transformations of functions".

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