Restrict $x$ in an equation, but keeping only one equation How do you put restrictions on the $x$ in an equation without writing more than one equation? This is a two part question:


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*How to take out a section of the graph of an equation?

*How to take out everything but a section of the graph of an equation?


For example, to take out $x$ from $-1$ to $1$ in $y=|x|$, you can change the equation to $$y=|x|\times\dfrac{\sqrt{|x|-1}}{\sqrt{|x|-1}}$$
I need to take a function, say $f(x)$, and restrict it to $1 < x < 4$.

You're on the right track. If you want to restrict the domain to $1 < x < 4$, simply multiply and divide by square root which would imply the two separate restrictions $x>1$ and $x<4$. In this case. Those would be $\sqrt{x-1}$ and $\sqrt{4-x}$. Put it all together and you have

 $f(x)_{restricted} = f(x) \cdot \frac{\sqrt{x-1}}{\sqrt{x-1}} \cdot \frac{\sqrt{4-x}}{\sqrt{4-x}}$.

The process for eliminating everything but a certain region is similar.
