what type from f x to g x on the graph ?
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When looking at the graph, we can discard two of the options, rotation (as they don't have any intersection, there are no possibilities of having a rotation axis) and reflection. It occured a translation. To know which of the options is correct, we can see the y intercepts of both lines. The y intercept of f(x) is 0 and the y intercept of g(x) is -4, which means that the line was translated down 4 units.
It means the right answer is D. Vertical Translation down 4 units.