Question

determine the end behavior for the following graph.
a. as $x\to\infty, y\to-\infty$ and as $x\to-\infty, y\to\infty$
b. as $x\to\infty, y\to-\infty$ and as $x\to-\infty, y\to-\infty$
c. as $x\to\infty, y\to\infty$ and as $x\to-\infty, y\to\infty$
d. as $x\to\infty, y\to\infty$ and as $x\to-\infty, y\to-\infty$
answer attempt 1 out of 2
a b
c d

Explanation:

Step1: Analyze right end behavior

As \( x \to +\infty \), observe the graph's right end. The line goes downward, so \( y \to -\infty \).

Step2: Analyze left end behavior

As \( x \to -\infty \), observe the graph's left end. The line goes upward, so \( y \to +\infty \).

Step3: Match with options

Option A states "as \( x \to \infty, y \to -\infty \) and as \( x \to -\infty, y \to \infty \)", which matches our analysis.

Answer:

A. as \( x \to \infty, y \to -\infty \) and as \( x \to -\infty, y \to \infty \)