Using translation concepts, it is found that the transformations needed to form g(x) = 3(x + 2)² - 1 from f(x) = x² are given as follows:
- The graph of g(x) is narrower than f(x), and is shifted to left 2 units and down 1 unit.
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the change is as follows:
f(x) = x² -> g(x) = 3(x + 2)² - 1.
f(x) is multiplied by 3 to form g(x), hence g(x) has a narrower graph. Since x -> x + 2, it was shifted left 2 units, and since y -> y - 1, it was shifted down 1 unit.
More can be learned about translation concepts at https://brainly.com/question/4521517
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