<s>[INST] How to get a whole number from $y = \frac{1}{x + 2}$ How to come up with a whole number for y.
I keep coming up with fractions from $y = \frac{1}{x +2}$ 
I've tried numerous numbers, as in, $ 1, 2, 3 ,4 , 5, -1, -2, -3, -4, -5$.
For example, $y = \frac{1}{1 + 2} = \frac{1}{3}$.
It's suppose to make two separate identical  curves on a Cartesian plane, and one is positive and negative, the other is in the negatives. When the $x$ values are positive, the $y$ value is less then $1$. When the $x$ value is negative the $y$ value goes greater then $1$.
 [/INST] Because the numerator is $1$ in this case, using whole numbers for $x$ the only way that the fraction $\frac{1}{x+2}$ can be a whole number is when the denominator is either $1$ or $-1$. Knowing this, the only solutions are when $x$ is either $-1$ or $-3$. This gives us $y$ values of $1$ and $-1$ respectively.

If you just want $y$ to be an integer, but you don't need $x$ to be an integer, you could first solve your function for $x$ like this:
$$
  y = \frac{1}{x+2} \qquad\implies\qquad x = \frac{1-2y}{y}
$$
Now supposing you want the $y$-value of your original function to be $y=5$, you just evaluate this new form at $y=5$ and find $x$, so
$$
  x = \frac{1-2y}{y} = \frac{1-2(5)}{(5)} = -\frac{9}{5}\;.
$$
So the $x$-value of $-9/5$ evaluates to $5$ when used in your original function.
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