Question

the graph shows a piecewise function. whats the end behavior of the function?
a. as x approaches -∞, f(x) approaches +∞, and as x approaches +∞, f(x) approaches -∞.
b. as x approaches -∞, f(x) approaches -∞, and as x approaches +∞, f(x) approaches -∞.
c. as x approaches -∞, f(x) approaches -∞, and as x approaches +∞, f(x) approaches 0.
d. as x approaches -∞, f(x) approaches 0, and as x approaches +∞, f(x) approaches +∞.

Explanation:

1. Observe the left end of the graph: as $x$ moves towards $-\infty$, the function values trend downwards to $-\infty$.
2. Observe the right end of the graph: as $x$ moves towards $+\infty$, the function values trend downwards to $-\infty$.
3. Match this behavior to the given options.

Answer:

B. As $x$ approaches $-\infty$, $f(x)$ approaches $-\infty$, and as $x$ approaches $+\infty$, $f(x)$ approaches $-\infty$.