1) what kind of functions are the following equations:

a) x-12.4=-\left(0.5y-0.8\right)^{2}\left\{12.307\le x\right\}\left\{1.6153\le y\right\}

b) x-13.54=0.38\sin\left(1.1y-6\right)\left\{11.306\le y\le12.66\right\}

c) y-5.63=\sqrt{8\left(x-8\right)}\left\{19.017\le x\le21.129\right\}

d) \frac{\left(x-10.9\right)^{2}}{1.2}+\left(y-16.7\right)^{2}=1.7\left\{x\le9.675\right\}\left\{y\le16.95\right\}

e) y=z\frac{1}{9}\frac{1}{5\left(x+10\right)}+75\ \left\{-11<x<-9\right\}\left\{76.5>y>73.4\right\}

2) How would you transform the equations below to reflect them over the y- axis?

first, #2. reflecting across the y-axis makes f(x) into f(-x)

Now, why don't you write these fractions using the normal text and parentheses, as in
y = z/9 * 1/(5(x+10)
and so on. The TeX or whatever you are using is very annoying.