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Answer:
Option C.
Step-by-step explanation:
we know that
The equation of the parent function f(x) (red graph) is
This is a vertical parabola open upward
The vertex is the point (0,0) (the origin)
The function g(x) (blue graph) is a vertical parabola open upward
The vertex is the point (-5,0)
The transformation of f(x) to g(x) has the following rule
f(x) -----> g(x)
(0,0) ----> (-5,0)
(x,y) ----> (x-5,y)
That means----> The transformation is a translation of 5 units at left
therefore
The equation of g(x) is
The statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.
<h3>What is polynomial?</h3>Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
We have a polynomial function:
The function is a cubic function and the graph of the cubic function will be a curve.
As we can see in the graph, f(x) grows larger as x approaches negative infinity. f(x) also becomes closer to infinity as x does.
Thus, the statement (A) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity is correct.
Learn more about Polynomial here:
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