Answer:
(d) k = 8
Explanation:
The value k in the equation ...
g(x) = f(x) +k
represents a vertical translation by k units.
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The vertex coordinates for f(x) and g(x) are ...
f(x): vertex = (-3, -3)
g(x): vertex = (-3, 5)
This means ...
f(-3) = -3
g(-3) = 5 = f(-3) +k = -3 +8 ⇒ k = 8
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Additional comment
Translations of various kinds are often most easily seen by comparing points where the graph has a distinctive feature. On this graph, that is the vertex.