Domain and Range

"Domain" and "range" are just two different words for "how far something extends"; specifically, a king's domain is the territory he controls, and an animal's range is the region it wanders through. So it makes some sense that the set of numbers a function "controls" would be called its domain, and the set through which its value can wander is called its range.1

1.http://mathforum.org/library/drmath/view/62497.htm

Domain represents all the x values, and Range represents all the y values. List the x and y values without duplication.

Ex: State the Domain and Range of the following relation.

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

Domain: {2, 3, 4, 6}
Range: {–3, –1, 3, 6}

http://www.purplemath.com/modules/fcns2.htm

What is a function?
If you can solve for “y”, then it is a function or if you can enter it into your graphing calculator. You can also tell if it’s a function by using the vertical line test. If it crosses through the graph twice, it is not a function.

1. This one is a function because there is no vertical line that will cross this graph twice.

2. This one is not a function because any number of vertical lines will intersect this oval twice. For instance, the y-axis intersects twice.
http://www.purplemath.com/modules/fcns.htm

Finding the Domain

The domain of a function is the set of numbers that you can put into the function and get out something that makes sense.

Ex: f(x) = (4+x)/(x^2-9)

(1) If we put in 4, we get f(4) = (4+4)/(4^2 - 9) = 8/7.

(2) If we put in 0, we get f(0) = (4+0)/(0^2 - 9) = 4/-9 = -(4/9)

(3) If we put in 3, we get f(3) = (4+3)/(9-9) = 7/0

You can't divide by 0, so 7/0 is an answer that doesn't make sense, and that f(x) is not defined at x = 3 and the same for x = -3. You will always get a fraction out of this function. (If you get a whole number n, you can think of it as the fraction n/1.) The only fractions that are undefined are those with 0 in their denominators.

This means that the function is undefined only at these two numbers, so its domain is all real numbers but 3 and -3.

http://mathforum.org/library/drmath/view/54554.html

Domain and Range by Semba04

Domain is associated with 'x' and
Range is associated with 'y'
always remember that!
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A relation is a set of ordered pairs (if you have a line or points on a graph you can have ordered pairs).

ex. (x, y), (3, 5), (4, -6), (-3, -1)

Domain is all the x values of a relation.

D = {x, 3, 4, -3}

Range is all the y values of a relation.

R: {y, 5, -6, -1}

Curly brackets are used to name the ordered pairs. I believe an = and : can be used interchangeably.


A function is when the x and y variables have something common and can be found using an equation.


Vertical Line Test
If a vertical line can be drawn to intersect more than exactly one point on a relation then that relation cannot be a function because it fails the vertical line test.

This states that if a line intersects its self on the (lets say) x axis it fails the vertical line test, so it is not a function.
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The relation of this diagram is:
(1, 5), (2, 6), (3, 5), (4, 6)
D: {1, 2, 3, 4}
R: {5, 6, 5, 6}
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This is a function
D: {'infinite'}
R: {'infinite'}
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This is not a function
D: {0, >5}
The domain is larger than zero
R: {0, >6}
The range is less than six
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This is a function
D: {<-5.5,>5.5}
R: {<0,>-5.5}
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This is not a function
D: {'infinite'}
R: {'infinite'}

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This is a function (notice how the circle on the bottom is not filled and the one on the top is. If the circle on the bottom was filled this would not be a function because those two points would overlap)
D: {<-6, >6}
R: {<-6, >6}
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Links for your knowledge (or entertainment): :)
Math Demos
Free Math Help
Bellingham High School Math
Purple Math

Everyting on this post was typed by me, by myself accept the vertical line test which I took from my notes from last year.

October 4 and 5

What to do....according to my in-class discussion:

Domain and Range

The domain of a function is all the possible x values which will make the function "work" by outputting real values.

When finding the domain, remember:
denominator (bottom) of a fraction cannot be zero
the values under a square root must be positive

The range of a function is the possible y values of a function resulting when we substitute all the possible x-values.

When finding the range, remember:
substitute different x-values into the expression for y to see what is happening
make sure you look for minimum and maximum values of y

You may even want to draw a sketch of the graph.

http://www.intmath.com/Functions-and-graphs/2a_Domain-and-range.php

Domain= D=(x)
Range=R=(y)

Example: (2,4),(2,7),(5,6),(3,8)

D=(x) so the domain must be; {2,2,5,3}

R=(y) so the range must be;{4,7,6,8}



Take the graph: y=2-x



The x-intercept is at (2,0) and the y-intercept is at (0,-2)






Domain- x1,x2, all real numbers

Range-y1,y2, all real numbers

So from the graph above the Domain and range would be:

D= {2,0}

R= {0,-2}

http://block5applied.blogspot.com/

Some Links that you may find helpful are:

http://www.purplemath.com/modules/fcns2.htm

http://www.freemathhelp.com/domain-range.html

http://mathdemos.gcsu.edu/mathdemos/domainrange/domainrange.html

http://mathforum.org/library/drmath/sets/select/dm_domain_range.html