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Answer:
The vertex of g(x) is (-4, -2)
Step-by-step explanation:
Let's define general translations:
Vertical translation:
For a function f(x), a vertical translation of N units (So the whole graph of f(x) is translated N units in a given direction) is defined as:
g(x) = f(x) + N
such that:
If N is positive, the translation is upwards
if N is negative, the translation is downwards.
Horizontal translation:
Similar than before, for a function f(x) a horizontal translation of N units is written as:
g(x) = f(x + N)
Where, if N is positive, the translation is to the left
If N is negative, the translation is to the right.
Here, we have the transformation:
g(x) = f(x - 2) - 5
This is a transformation that moves the whole graph of f(x):
2 units to the right
5 units downwards.
So, if a point like (x, y) was in the graph of f(x)
After the translation, that point will be (x + 2, y - 5)
Then, if the original vertex was (-6, 3), the new vertex will be:
(-6 + 2, 3 - 5)
(-4, -2)
The vertex of g(x) is (-4, -2)