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

Question

shadowfiend · Answer

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

anonymous · Answer

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?

anonymous · Answer

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

shadowfiend · Answer

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.

anonymous · Answer

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

shadowfiend · Answer

f.

anonymous · Answer

Okay thanks!

shadowfiend · Answer

No problem!