Mathematics 20 Online
OpenStudy (anonymous):

Determine the domain or range of a function---I need help!

Can you post which function you're trying to find the domain/range of?

OpenStudy (anonymous):

I tell my students, domain is all values of x that don't "cause problems" for the function. Problems include negatives inside square roots, dividing by zero, etc. A function like y = 2x + 1 has no problems, so the domain is all real numbers. A function like $y=1/(x^2-1)$ can't have division by zero, so we must exclude 1 and -1; therefore, the domain is all real numbers except 1 and -1. A function like $y=\sqrt{4-x^2}$ has a problem whenever 4 - x^2 is negative, so all those values of x must be excluded. Range is for y, and it's all the y values that are produced by the function. Suppose you have the function y = x^2, a parabola. Since all squares are positive, there is no way for the function to produce a negative value for y. Therefore the range is all non-negative real numbers. That help?

OpenStudy (anonymous):

Well my problem is: What is the domain of the function f(x)= 1/3 x + 3 when the range is {0, 3, 6} ?

So in this case, you have the values of $$y$$ (or in this case, $$f(x)$$), and you want to find the valid values of $$x$$. To do that, you just solve the three equations with $$f(x)$$ set to each of the three values they give you for the range, and the values of $$x$$ for those equations will be the domain of the function.

OpenStudy (anonymous):

So I have to replace f or x with one of the three numbers {0,3,6} ?

f.

OpenStudy (anonymous):

Okay thanks!