Question

f(x) g(x) ​ =x 2 =(x+4) 2 −1 ​ We can think of g gg as a translated (shifted) version of f ff. Complete the description of the transformation. Use nonnegative numbers. To get the function g gg, shift f ff up/down by units and to the right/left by units.

Answer 1

To transform f(x) into g(x), the function f(x) must be shifted to the left by 4 units and shifted downward by 1 unit.

Step-by-step explanation:

When comparing the function f(x) = x2 to g(x) = (x+4)2 - 1, we can observe that g(x) is a transformation of f(x). Specifically, to transform f(x) into g(x), the function f(x) is shifted to the left by 4 units (since x is replaced by x+4) and shifted downward by 1 unit (because of the -1 term in g(x)). This can be determined by understanding how horizontal shifts and vertical shifts affect the graph of a function.