**Transformations of Functions : **

In this section, we will learn, how to do different types of transformations of functions like translation, stretch, compression and reflection.

To make the students to understand the different types of transformations, we have explained each kind of transformation with step by step explanation along with the corresponding figures.

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.

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

**3. Reflection through the x-axis **

**4. Reflection through the y-axis**

**5. Horizontal Expansions and Compressions**

**6. ****Vertical Expansions and Compressions**

How different types of transformations occur in terms of x-coordinate and y-coordinate have been summarized below.

**Summary of Transformation**

**Transformation**

**Appearance in Function**

**Transformation of Point**

Vertical Translation

f(x) ---> f(x) + d

(x, y) --> (x, y + d)

Horizontal Translation

f(x) ---> f(x - c)

(x, y) --> (x + c. y)

Vertical Stretch or Compression

f(x) ---> af(x)

(x, y) --> (x, ay)

Horizontal Stretch or Compression

f(x) ---> f(kx)

(x, y) --> (x/k, y)

Reflection in x-axis

f(x) ---> -f(x)

(x, y) --> (x, -y)

Reflection in y-axis

f(x) ---> f(-x)

(x, y) --> (-x, y)

In transformations of functions, if we have more than one transformations, we have to do the transformations one by one in the following order.

1. Stretches / Compressions

2. Reflections

3. Translations

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 the following questions.

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, how to do transformations of functions.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**