Answer: Choice D. -f(x-3)
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Explanation:
Imagine that we're able to move the xy grid freely but keep the f(x) curve fixed in place. Now imagine that we move the xy grid 3 units to the left. This would give the illusion the f(x) curve moves 3 units to the right.
If we replace each input x with x-3, then that will effectively move the xy grid 3 units to the left. So that's why f(x-3) is a translation of 3 units to the right.
The negative out front will reflect the curve over the x axis. Points of the form (x,y) become (x,-y). For example, if (1,2) is on the curve then (1,-2) is on the reflected curve.
Putting this all together and it leads us to -f(x-3) which is choice D.
