Why would $(x+1)$ transform the graph to the left? 
Why do transformations for the $x$ variable in graphs work opposite as you would expect?

Example: $f(x) =(x)-1$ moves the graph down as you would expect but $g(x) = (x+1)-1$ moves the graph down (as it looks like) but instead of to the right one it's to the left one. 
Note: I understand fully how to do graph transformations but don't understand why we just deem the x-value transformations as "doing the opposite".
Thanks!
 A: Look at the objects in front of yourself. Now take a step to the right. The objects shifted to the left, not right, right?
A: Because your domain values will decrease by $1$ in order to provide the same output.
Let’s say for $f(x)$, we have the following points:
$$(x_1, y_1), (x_2, y_2), (x_3, y_3)$$
Now, if we have $f(x+1)$, our inputs will all decrease by one.
$$(x_1-1, y_1), (x_2-1, y_2), (x_3-1, y_3)$$
Obviously, the $-1$ balances the $+1$ in $f(x+1)$.
Therefore, this explains why we carry out the opposite operation to those in the parentheses. In a more general form, we get the following rule.  
For positive values of $n$, shift $n$ units left for $f(x+n)$ and shift $n$ units right for $f(x-n)$.
For multiplication and division within the parentheses, the idea is exactly the same.
For values of $n$, there will be horizontal stretch by scale factor $\vert{\frac{1}{n}}\vert$ for $f(nx)$, and there will be horizontal stretch by scale factor $\vert n\vert$ for $f(\frac{x}{n})$.
A: One thing to notice is that in an equation like
$$y=(x+1)^2 - 2$$
the 1 is with the $x$, but the $-2$ is on the opposite side
of the equal sign from $y$.  This $-2$ moves the graph down,
but put it on the other side of the equation and you have
$$y+2 = (x+1)^2.$$
So things are more symmetric than you thought.  Pluses move things in the negative direction.
Next, if you think of a graph drawing machine that's going to draw the graph of $y=f(x)$ from left to right, then what happens when you increase $x$ by $1$?  Everything happens 1 unit sooner.  $x$ may be at $7$, but the function is being fed $8$, so the point that used to be at $8$ is now at $7$.  Everything is shifted left.
