Let's identify the functions that have the given properties step by step:
### Property 1: The domain is all real numbers.
Solution: The function satisfying the property that the domain is all real numbers is represented by [tex]$1$[/tex]. Therefore, the function with the domain of all real numbers is labeled as [tex]$\boxed{1}$[/tex].
### Property 2: An [tex]\( x \)[/tex]-intercept is [tex]\((\pi, 0)\)[/tex].
Solution: The function satisfying the property where the [tex]\( x \)[/tex]-intercept is [tex]\((\pi, 0)\)[/tex] is represented by [tex]$2$[/tex]. Thus, the function with an [tex]\( x \)[/tex]-intercept at [tex]\((\pi, 0)\)[/tex] is labeled as [tex]$\boxed{2}$[/tex].
### Property 3: The minimum value is -1.
Solution: The function satisfying the property where the minimum value is -1 is represented by [tex]$3$[/tex]. Therefore, the function with a minimum value of -1 is labeled as [tex]$\boxed{3}$[/tex].
### Property 4: An [tex]\( x \)[/tex]-intercept is [tex]\(\left(\frac{\pi}{2}, 0\right)\)[/tex].
Solution: The function satisfying the property where the [tex]\( x \)[/tex]-intercept is [tex]\(\left(\frac{\pi}{2}, 0\right)\)[/tex] is represented by [tex]$4$[/tex]. Thus, the function with an [tex]\( x \)[/tex]-intercept at [tex]\(\left(\frac{\pi}{2}, 0\right)\)[/tex] is labeled as [tex]$\boxed{4}$[/tex].
In summary:
- The function with a domain of all real numbers is [tex]$\boxed{1}$[/tex].
- The function with an [tex]\( x \)[/tex]-intercept at [tex]\((\pi, 0)\)[/tex] is [tex]$\boxed{2}$[/tex].
- The function with a minimum value of -1 is [tex]$\boxed{3}$[/tex].
- The function with an [tex]\( x \)[/tex]-intercept at [tex]\(\left(\frac{\pi}{2}, 0\right)\)[/tex] is [tex]$\boxed{4}$[/tex].
