Question

I really don’t get this question can someone help me

Answer 1

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