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earnstyle [38]
3 years ago
14

The function f(x)=3 (x+6)^2+8 is shifted 4 units up and 3 units right to form another function g(x). What is g(x)?

Mathematics
1 answer:
iVinArrow [24]3 years ago
3 0

Answer:

g(x) = 3\cdot (x+3)^{2}+12

Step-by-step explanation:

There are two operations involved:

Vertical translation:

f'(x) = f(x) \pm c,\,c\in \mathbb{R} (1)

Note: Positive sign represent a translation upwards.

Horizontal translation:

f'(x) = f(x\pm c), x\in \mathbb{R} (2)

Note: Positive sign represent a translation leftwards.

Then, the new function must be:

g(x) = f(x-3)+4

g(x) = 3\cdot (x+3)^{2}+12

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