Answer:
Option A. As x approaches negative infinity, f(x) approaches negative infinity.
Explanation:
The end behavior of a continuous function, whose domain is all real values, such as the absolute value function, is the limits of the function as x approaches negative and positive infinity.
In the graph, it is shwon that the absolute value function has a maximum of 5 at x = -4.
To the left of x = -4, the graph decreases linearly, meaning that the more negative x becomes, the more negative the value of the function becomes. That is "as x approaches negative infinity, f(x) approaches negative infinity", which is the option A.
The option B is incorrect because it is the the opposite of the option A.
Option C is incorrect, because to the right of x = - 4, as x approaches positive infinity, f(x) decreases linearly, approaching negative infinity, which is the opposite of what this choice states.
Option D is incorrect, because nothing indicates that f(x) in no longer continuos as x grows toward positive infinity; on the contrary, the question and the drawing suggest that the function is continuos for all the domain (-∞, +∞).
The statement that best describes the end behavior of this absolute value function is; A. As x approaches negative infinity, f(x) approaches negative infinity.
The end behavior of a continuous function, that has its' domain as all real values like absolute value function, is the limits of the function as x approaches -∞ and +∞.
Now, from the given graph, we see that the absolute value function has a maximum of 5 at the point x = -4.
At the left hand side of x = -4, we see the graph decreasing linearly. Thus, as x approaches -∞, f(x) approaches -∞.
The only option that corresponds to the above answer is Option A.
Read more about Function Graphs at; https://brainly.com/question/4025726
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