Question

determine the end behavior of the following function.
a. as x approaches positive and negative infinity, the function approaches ( y = 24 ).
b. as x approaches positive infinity, the function approaches ( y = 24 ).
as x approaches negative infinity, the function approaches ( y = 2 ).
c. as x approaches positive and negative infinity, the function approaches ( y = 12 ).
d. as x approaches positive infinity, the function approaches ( y = 24 ).

Explanation:

Step1: Analyze the graph

The horizontal asymptote of a function determines its end - behavior. A horizontal asymptote is a horizontal line \(y = k\) that the graph of the function approaches as \(x\to\pm\infty\).

Step2: Identify the horizontal asymptote

Looking at the graph, as \(x\to+\infty\) and \(x\to-\infty\), the function approaches the line \(y = 12\).

Answer:

C. As \(x\) approaches positive and negative infinity, the function approaches \(y = 12\).