lemme do the 5) first, since it's too simple.
a function proper, has a graph that passes the vertical line test, for points wise, that simply means that it will not have any x-coordinates repeated, so nothing like (1, 3) and (1, 4), because 1 is there twice, so x = 1 on those points, so that's not a function, a function cannot have repeated x-coordinates.
when a graph of a function touches the y-axis, at that moment x = 0, and if that graph is of a function, "x" will be 0 only once, so the y-axis intersection for a function will only happen once.
2)
notice all those denominators, now, their LCD will be 12 for all those, you can check, 12 is divisible by all four denominators.
anyway, let's multiply both sides by the LCD of 12, to do away with the denominators and then simplify.
[tex]\bf \stackrel{\textit{multiplying both sides by 12}}{12\left( \cfrac{3}{2}+\cfrac{2}{3}w \right)=12\left( \cfrac{1}{4}w-\cfrac{1}{2} \right)}\implies 18+8w=3w-6
\\\\\\
5w=-24\implies w=-\cfrac{24}{5}[/tex]
