Mappings between intervals

Find functions that map:

Variant 1
The interval \((0{,}1)\) to the interval \((0,\infty)\).
Hint
Use the properties of trigonometric functions, or possibly a reciprocal function.
Result
\(\frac{1}{\sin(\pi x)}-1\), for example.
Variant 2
The interval \((0{,}1)\) to the interval \((-\infty,\infty)\).
Resolution
\(\tan\left(\left(x-\frac12\right)\pi\right)\), for example.
Variant 3
The interval \((0{,}1)\) to the interval \(\langle0{,}1\rangle\).
Result
\(|\sin(10 x)|\), for example.
Variant 4
The interval \(\langle 0{,}1\rangle\) to the interval \(\langle 0,\infty)\).
Result
\(\frac{1}{\sin(\pi x)}-1\), for example.
Variant 5
The interval \((0,\infty)\) to the interval \((0{,}1)\).
Result
\(\frac{1}{x+1}\), for example.