Question

Beginning with the graph of f(x)= x², what transformations are needed to form g(x)=3(x+2)^2-1 ?

Answer 1

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 brainly.com/question/4521517

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