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.
Question :
Perform the following transformation to the function y = √x.
"a horizontal expansion 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
Answer :
Step 1 :
Since we do horizontal expansion 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 expanding 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 expansion made by the factor "0.5".
How to sketch the graph of the function which is horizontally expanded 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 expansion 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 expanded 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 expanded graph.
The same procedure to be followed for horizontal compression.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
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
Markup and markdown word problems
Word problems on mixed fractions
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
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
©All rights reserved. onlinemath4all.com
May 23, 22 01:59 AM
Exponential vs Linear Growth Worksheet
May 23, 22 01:59 AM
Linear vs Exponential Growth - Concept - Examples
May 23, 22 01:34 AM
SAT Math Questions on Exponential vs Linear Growth