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Can you give good definitions for domain and range of functions?

- HomeschoolingMom
**Posts:**1**Joined:**Sun Mar 24, 2013 5:06 pm

Definitions for Domain and Range are well given in textbooks on Intermediate and College Algebra. Domain is the set of values that a function can accept. Range is the set of values which the function can have. Those are about as simply stated as they can be.

A clearer imaging of the concepts will come from seeing a few examples. Using f(x)=mx+b, where x is the independant variable, m and b are not zero, x can be any Real number. You can say the domain of f(x) is the Real Numbers. Using p(x)=0.25x-12, this function again can take any Real number as input, or value for x. Using v(x)=x-6, the domain of v(x) is the Real Numbers. If you have some function, g(x)=(0.25x-12)*(x-6)/(x-6), your first thought might just be, "just simplify it and you have g(x)=0.25x-12"; but that is not the function given as g(x). If you examine the righthand member for g(x)=(0.25x-12)*(x-6)/(x-6), and then ask, "what is the set of values which x can be in g(x)?", the response is, "g(x) can accept Real Numbers such that x<>6". The DOMAIN of g(x) is the Real Numbers, EXCEPT THAT x<>6. Further, you may say that the RANGE for g(x) must EXCLUDE -10.5, because that is the missing point for x=6. Recall, x<>6.

A clearer imaging of the concepts will come from seeing a few examples. Using f(x)=mx+b, where x is the independant variable, m and b are not zero, x can be any Real number. You can say the domain of f(x) is the Real Numbers. Using p(x)=0.25x-12, this function again can take any Real number as input, or value for x. Using v(x)=x-6, the domain of v(x) is the Real Numbers. If you have some function, g(x)=(0.25x-12)*(x-6)/(x-6), your first thought might just be, "just simplify it and you have g(x)=0.25x-12"; but that is not the function given as g(x). If you examine the righthand member for g(x)=(0.25x-12)*(x-6)/(x-6), and then ask, "what is the set of values which x can be in g(x)?", the response is, "g(x) can accept Real Numbers such that x<>6". The DOMAIN of g(x) is the Real Numbers, EXCEPT THAT x<>6. Further, you may say that the RANGE for g(x) must EXCLUDE -10.5, because that is the missing point for x=6. Recall, x<>6.

- jg.allinsymbols
**Posts:**71**Joined:**Sat Dec 29, 2012 2:42 am

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