Grade 11 Functions - Would you please check my answers to a couple questions? My teacher didn't put up the answers anywhere but I'm still paranoid about getting the questions wrong. I guess my teacher's not worried about it because the questions are fairly easy? The original graph is $y=f(x)$. "Shift left 3 units" has the equation $y = f(x+3)$
Also, $y = f(x-2)$ means "horizontal translation of 2 units to the right?"

Yes, that's correct. There is an easy way to remember this:
Take $y = f(x+3)$. If you set $x = -3$, then $f(x+3) = f(-3+3) = f(0)$. That means: The image of $0$ (= the value of $f(0)$) moved from $x=0$ to $x = -3$. So it moved three units to the left.
Now take $y = f(x-2)$. If you set $x = 2$, then $f(x-2) = f(2-2) = f(0)$. That means: The image of $0$ (= the value of $f(0)$) moved from $x=0$ to $x = 2$. So it moved two units to the right.
