# Domain And Range

• May 3rd 2008, 07:41 PM
subzero06
Domain And Range
hello, i need some help with this problem please!!:

Given

y= 1/x-3

a)find the domain
b)find the range

thanks
(Wondering)
• May 3rd 2008, 08:32 PM
Reckoner
Quote:

Originally Posted by subzero06
y= 1/x-3

Do you mean $\displaystyle y = \frac{1}{x} - 3$ (as it's written) or $\displaystyle y = \frac{1}{x - 3}$?

In either case, the domain is the set of values of $\displaystyle x$ for which the function is defined. Notice that you have a variable in the denominator of your function. Since division by zero is undefined, what does that tell you about the values that $\displaystyle x$ can take on?

The range will be all of the possible values of $\displaystyle y$. For $\displaystyle y = \frac{1}{x} - 3$, note that $\displaystyle \frac{1}{x}$ can never be zero; what does that tell you about the possible values of $\displaystyle y$?
• May 3rd 2008, 09:20 PM
subzero06
Quote:

Originally Posted by Reckoner
Do you mean $\displaystyle y = \frac{1}{x} - 3$ (as it's written) or $\displaystyle y = \frac{1}{x - 3}$?

In either case, the domain is the set of values of $\displaystyle x$ for which the function is defined. Notice that you have a variable in the denominator of your function. Since division by zero is undefined, what does that tell you about the values that $\displaystyle x$ can take on?

The range will be all of the possible values of $\displaystyle y$. For $\displaystyle y = \frac{1}{x} - 3$, note that $\displaystyle \frac{1}{x}$ can never be zero; what does that tell you about the possible values of $\displaystyle y$?

yeah the second 1
y=1/(x-3)

so X cannot be 3? so is any number not = 3?
and Y is any number but not zero?
• May 3rd 2008, 09:22 PM
mr fantastic
Quote:

Originally Posted by subzero06
yeah the second 1
y=1/(x-3)

so X cannot be 3? so is any number not = 3?
and Y is any number but not zero?

Yes.
• May 3rd 2008, 09:31 PM
Reckoner
Quote:

Originally Posted by subzero06
yeah the second 1
y=1/(x-3)

so X cannot be 3? so is any number not = 3?
and Y is any number but not zero?

Correct! The domain is all real numbers $\displaystyle x\neq3$, and the range is all real numbers $\displaystyle y\neq0$. Good job.