HORIZONTAL TRANSLATIONS OF FUNCTIONS
Horizontal Translations of Functions :
In function graphing, a horizontal translation is a transformation that shifts the original graph either to the right side or left side by some units.
Horizontal Translation - Definition
A horizontal translation "slides" an object a fixed distance either on the right side or left side. The original object and its translation have the same shape and size, and they face in the same direction.
In simple words, horizontal translation means, it just moves the given figure either on the right or left without rotating, re-sizing or anything else.
Horizontal Translations of Functions - Rule
Let y = f(x) be a function and "k" be a constant.
In the above function, if "x" is replaced by "x-k" , we get the new function
y = f(x - k)
The graph of y= f(x-k) can be obtained by the translating the graph of y = f(x) to the right by "k" units if "k" is a positive number.
In case "k" is a negative number, the graph of y = f(x) will be translated to the left by |k| units.
Moreover, if the the point (x,y) is on the graph of y = f(x), then the point (x+k , y) is on the graph y = f(x-k).
For example, if k =3, the graph of y = f(x) will be translated to the right by "3" units.
If k = -3, the graph of y = f(x) will be translated to the left by "3" units.
Horizontal Translation - Example
Once students understand the above mentioned rule which they have to apply for horizontal translation, they can easily make horizontal translations of functions.
Let us consider the following example to have better understanding of horizontal translation of a function.
Question :
Perform the following transformation to the function
y = √x.
"a translation to the right by 3 units"
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 a translation to the right by "3" units, we have to replace "x" by "x-3" in the given function y = √x.
Step 2 :
So, the formula that gives the requested transformation is y = √(x-3)
Step 3 :
The graph y = √(x-3) can be obtained by translating the graph of y = √x to the right by "3" units.
Step 4 :
The graph of the original function (given function)
Step 4 :
The graph of the transformed function.
After having gone through the stuff given above, we hope that the students would have understood, how to do horizontal translation of a function.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
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
Recent Articles
-
Practice Problems on Whole Numbers
Jan 18, 20 08:53 AM
Practice Problems on Whole Numbers - Practice problems in the form of test with solution
-
How to Solve Word Problems Involving Speed
Jan 18, 20 08:34 AM
How to Solve Word Problems Involving Speed - Concept and example problems with step by step solution
-
Math Olympiad Sample Problems 6th Grade
Jan 18, 20 07:33 AM
Math Olympiad Sample Problems 6th Grade - Problems with step by step solution
