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 2 out of 2 a b c d

Explanation:

Step1: Analyze right end behavior

As \( x \to +\infty \), observe the graph's right - most arrow. The line is increasing, so \( y \to +\infty \).

Step2: Analyze left end behavior

As \( x \to -\infty \), observe the graph's left - most arrow. The line is decreasing, so \( y \to -\infty \).
Now check the options:

• Option A: \( \text{as } x\to\infty,y\to -\infty \) (wrong, should be \( y\to+\infty \)) and \( \text{as } x\to -\infty,y\to\infty \) (wrong, should be \( y\to -\infty \)).
• Option B: \( \text{as } x\to\infty,y\to -\infty \) (wrong) and \( \text{as } x\to -\infty,y\to -\infty \) (wrong).
• Option C: \( \text{as } x\to\infty,y\to -\infty \) (wrong) and \( \text{as } x\to -\infty,y\to\infty \) (wrong).
• Option D: \( \text{as } x\to\infty,y\to\infty \) (correct) and \( \text{as } x\to -\infty,y\to -\infty \) (correct).

Answer:

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