DOMAIN AND RANGE OF RATIONAL FUNCTIONS WITH HOLES
About the topic "Domain and range of rational functions with holes"
"Domain and range of rational functions with holes" is a much needed stuff required by almost all the students who study math in high schools.
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 "Domain and range of rational functions with holes", we have given step by step explanation.
Domain of a rational function with hole
Let f(x) = (x² - x - 2) / (x-2)
Domain is nothing but the real values of "x" for which "f(x)" is defined.
In the above rational function, if we make the denominator x -2 equal to zero, we get x = 2
That is, x - 2 = 0 ===> x = 2
Hence, "y" is defined for all real values of "x" except x = 2
Hence, Domain (y) = R - {2}
Finding hole of a rational function
For the rational function f(x) = (x² - x - 2) / (x-2), let us try to find hole, if any.
To find hole, let us try to simplify the given rational function as given below.
In the above simplification, the common factor for numerator and denominator is (x-2). So there is a hole.
(Note : If there is no common factor for numerator and denominator, there is no hole)
Now we have to make the common factor (x-2) equal to zero.
When we do so, we get
x - 2 = 0 ===> x = 2
So, the hole is at x = 2
After having crossed out the common factor (x-2), the function is simplified to f(x) = x+1 or y = x+1.
Now, if we plug x = 2 in y = x+1, we get y = 3.
Hence, the hole appears on the graph at (2 , 3)
After simplification, the given rational function becomes y = x + 1 which is linear and its graph will be a straight line.
Graph of y=x+1
Range of a rational function with hole
When we look at the above figure, the graph of y= x+1 appears at every real value of "y" except at y = 3. Because, there is a hole at y = 3.
So, the range is all real values except "3".
More clearly, Range (y) = R - {3}
You can also visit the following sites to know more about domain and range of rational functions.
http://www.montereyinstitute.org
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
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
Recent Articles
-
How to Find Maximum and Minimum Value of a Function
Apr 02, 20 12:15 AM
How to Find Maximum and Minimum Value of a Function - Concept and examples with step by step explanation
-
Finding Maximum and Minimum Value of Quadratic Function
Apr 02, 20 12:13 AM
Finding Maximum and Minimum Value of Quadratic Function
-
Maximum and Minimum Values of Quadratic Functions Worksheet
Apr 01, 20 11:46 PM
Maximum and Minimum Values of Quadratic Functions Worksheet
