This is the original function; y=f(x) with a domain of -3<_ x <_ 3 and a range of 0 <_ y <_ 3.
Now I was asked to find the range and domain of y=f(x-2).
So I said -3<_ x <_ 3 and 1<_ y <_ 5.
But the answer was -1<_ x <_ 5 and 0 <_ y <_ 3.
I don't get it. Am I supposed to keep the same range, not the domain? Is that what it is? Why is my answer wrong?
Best Answer
The domain is the set of numbers you plug into $f$. Here, the number you plug into $f$ needs to be between $-3$ and $3$. Since the number you're plugging into $f$ is $x-2$, this means you need $-3 \le x-2 \le 3$, which is equivalent to $-1 \le x \le 5$.
The range is the set of values that the function $f$ takes; since $f(x-2)$ is simply a value of $f$ for each input $x$, the range of the new function is the same as the range of the old function.