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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?"

measure_theory
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Hamze
  • 39

1 Answers1

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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.

Algebrus
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