Mathematics High School

Which statement describes the end behavior of the function f(x) = 8|x − 1| + 13?

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 negative infinity.
D.
As x approaches positive infinity, f(x) is no longer continuous.

Answers

Answer 1

The statement that describes the end behavior of the function f(x) = 8|x − 1| + 13 is:

As x approaches positive infinity, f(x) approaches negative infinity.C.

Let's analyze the function.

The function f(x) = 8|x − 1| + 13 involves the absolute value of x − 1, which means that the expression inside the absolute value will always be non-negative.

x approaches positive infinity, the value of x − 1 also approaches positive infinity.

Since the absolute value of a positive number is equal to the number itself, we can simplify the expression to f(x) = 8(x − 1) + 13.

As x approaches positive infinity, the term 8(x − 1) becomes larger and larger, making f(x) approach negative infinity.

The constant term 13 does not have a significant impact on the end behavior as x becomes increasingly large.

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