Answer: Choice D. g(x) = 3|x-3| - 6
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Explanation:
Points are of the form (x,y), where y = f(x) since y and f(x) are outputs.
When we vertically stretch by a factor of 3, we are making the function curve 3 times more stretched out along the vertical y axis. So a general point (x,y) becomes (x,3y). Whatever the y coordinate is, we multiply by 3 to get its stretched out counterpart.
Eg: (0,-2) on f(x) moves to (0,-6) which is on g(x)
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Since y = f(x), and we're multiplying y by 3, we can say
f(x) = |x-3| - 2
3*f(x) = 3*( |x-3| - 2 )
3*f(x) = 3|x-3| + 3(-2)
3*f(x) = 3|x-3| - 6
g(x) = 3|x-3| - 6
