# INVESTIGATING HORIZONTAL STRETCHES COMPRESSIONS AND REFLECTIONS

Doing stretches, compressions and reflections horizontally are different types of transformations of functions.

To make the students to understand the stuff "Horizontal stretches, compressions and reflections",  we have explained the rule that we have to apply to make horizontal stretch, compression and reflection in a function.

## Horizontal Stretches and Compressions

Let y = f(x) be a function.

In the above function, if we want to do horizontal expansion or compression by a factor of "k", at every where of the function, "x" co-ordinate has to be multiplied by the factor "k". Then, we get the new function

y  =  f(kx)

The graph of y = f(kx) can be obtained by expanding or compressing the graph of  y = f(x) horizontally by the factor "k".

It can be done by using the rule given below.

Note :

Stretch and expansion mean the same thing.

## Horizontal Stretch - Example

Once students understand the above mentioned rule which they have to apply for horizontal stretch or compression, they can easily do this kind of transformations of functions.

Let us consider the following example to have better understanding of horizontal expansion.

Question :

Perform the following transformation to the function        y = √x.

"an horizontal strech by a factor 0.5"

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function

Solution :

Step 1 :

Since we do horizontal stretch by the factor "0.5", we have to replace  "x" by "0.5x" in the given function y = √x.

Step 2 :

So, the formula that gives the requested transformation is

y  =  √0.5x

Step 3 :

The graph y =  √0.5x  can be obtained by strtching the graph of the function y = √x horizontally by the factor 0.5.

(x, y) -------> (0.5x, y)

Step 4 :

The graph of the original function (given function)

Step 5 :

The graph of the function in which horizontal stretch made by the factor "0.5".

## How to sketch the graph of the function which is  horizontally stretched or compressed ?

Let "y = f(x)" be the given function and (x , y) by any point on the graph of the function y = f(x).

If we want to perform horizontal stretch in the graph of the function  y = f(x) by the factor "0.5", we have to write the point (x , y) as (0.5x ,  y).

That is, "x" co-ordinate of each and every point to be multiplied by the factor 0.5.

Therefore, any point on the horizontally stretched graph will be in the form of   (0.5x , y)

So, each and every point to be changed according to (0.5x , y) and plot them on the graph.

After having plotted the points, if we connect all the points, we will get the horizontally stretched graph.

The same procedure to be followed for horizontal compression.

## Reflections

Let y = f(x) be a function.

The graph of the function f(x) can be reflected about x- axis or y-axis or the line y = x or the line y = -x or the origin using the rules given below.

Based on the rules given above, the images and their reflections about x- axis and y-axis and the line y = x are given below.

Reflection about x - axis :

Reflection about y - axis :

Reflection about the line y = x :

Apart from the stuff given above, 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 the 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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6