Question

1. match the graph with the end behavior

_____ $f(x)$ approaches $-\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $-\infty$ as $x$ approaches $-\infty$.
_____ $f(x)$ approaches $-\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $\infty$ as $x$ approaches $-\infty$.
_____ $f(x)$ approaches $\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $-\infty$ as $x$ approaches $-\infty$.
_____ $f(x)$ approaches $\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $\infty$ as $x$ approaches $-\infty$.

Explanation:

Step1: Analyze end behavior of Graph A

As $x \to \infty$, the graph goes down ($f(x) \to -\infty$); as $x \to -\infty$, the graph goes up ($f(x) \to \infty$).

Step2: Analyze end behavior of Graph B

As $x \to \infty$, the graph goes up ($f(x) \to \infty$); as $x \to -\infty$, the graph goes up ($f(x) \to \infty$).

Step3: Analyze end behavior of Graph C

As $x \to \infty$, the graph goes down ($f(x) \to -\infty$); as $x \to -\infty$, the graph goes down ($f(x) \to -\infty$).

Step4: Analyze end behavior of Graph D

As $x \to \infty$, the graph goes up ($f(x) \to \infty$); as $x \to -\infty$, the graph goes down ($f(x) \to -\infty$).

Step5: Match descriptions to graphs

Pair each end behavior statement with the corresponding graph.

Answer:

C. $f(x)$ approaches $-\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $-\infty$ as $x$ approaches $-\infty$.
A. $f(x)$ approaches $-\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $\infty$ as $x$ approaches $-\infty$.
D. $f(x)$ approaches $\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $-\infty$ as $x$ approaches $-\infty$.
B. $f(x)$ approaches $\infty$ as $x$ approaches $\infty$, and $f(x)$ approaches $\infty$ as $x$ approaches $-\infty$.