Select the correct answer.

which statement describes the end behavior of this absolute value function?

a. as x approaches negative infinity, f(x) approaches negative infinity.

b. as x approaches negative infinity, f(x) approaches positive infinity.

c. as x approaches positive infinity, f(x) approaches positive infinity.

d. as x approaches positive infinity, f(x) is no longer continuous.

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 (-∞, +∞).