1. ## 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

2. Originally Posted by subzero06
y= 1/x-3
Do you mean $y = \frac{1}{x} - 3$ (as it's written) or $y = \frac{1}{x - 3}$?

In either case, the domain is the set of values of $x$ 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 $x$ can take on?

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

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

In either case, the domain is the set of values of $x$ 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 $x$ can take on?

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

4. 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.

5. 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 $x\neq3$, and the range is all real numbers $y\neq0$. Good job.