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Difference Between Domain and Range

Introduction to difference between domain and range

In difference between Domain and Range, domain is the set of all inputs for which the function is valid. The Range is the set of outputs that the function will be produce.

Domain=input = x

Range=output= y

The domain is all the possible x values, it can work for the equation, and the range is all the possible y values.

y = `1/x`, x can be all numbers, except for 0, y value from -1 to 1.

A Real-life Situation that could be Modeled by a Function to Illustrate Difference between Domain and Range:

Main difference between domain and range, domain is the set of numbers which are valid values for the independent variable. The range is the set of valid numbers for the dependent variable.

The angle of the sun over the horizon over the course of the day would be honestly easy to model. The domain can be the hours between sunrise and sunset and the range will be 0 to whatever is the maximum elevation of the sun is on a given day on any particular latitude. For cause, during the equinox, at latitude of 50 degree north, the maximum angle of the sun above the horizon is 40 degrees and therefore the range would be 0 to 40 degree. Notice that the range will increase during the summer and decrease during the winter.

The domain is valid value for the independent variable. The range is resulting dependent variable. This is the difference between domain and range.

So, let's function like y = 5+2x

Then the domain is values for x and the range is entire y, for corresponding values of all the 'x's. A function goes, you want to go to a local theme park. Tickets are $25 and parking is $10. The total price for a family is given by P=25a+10 where a is the number of people in the family. For that function the domain is all a values are positive (no family has 0 or negative number of members). The range is (35, 60, 85, 110,135,160 etc... like that). Now you find the difference between domain and range.

Examples of Difference between Domain and Range:

Ex1:

Find domain of function f(x) = `sqrt(x+2)`

Sol:

f(x) is not defined when (x + 2 ) is less than zero.

that is x + 2 should be greater than or equal to zero.

x `>=` -2

So, domain = All real numbers greater than or equal to -2.

y = `sqrt(x+2)`,

we can find Range by noticing that ( x +2 ) is taking only positive values.

there is no value of x for which we will get a negative value of y.

So Range of this function is all positive Real numbers.

Ex 2: Find the range of the function, y = `1/(x-1)`

we express x in terms of y.

since y = `1/(x-1)`

so, yx - y = 1

so, yx = y + 1

so, x = `(y+1)/y`

here we see that x is not defined when y = 0.

so Range of this function is all real numbers except 0, written as R - { 0 }


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