Question

Which statement is true about the end behavior of the

Answer 1

Answer:

End behavior :

1. As the x-values go to positive infinity, the function's values go to negative infinity

2. As the x-values go to negative infinity, the function's values go to positive infinity.

Option D: $f(x)$ over the interval $(-4,\infty).$  (answer for question in image)

Step-by-step explanation:

From the given graph it is clear that as the x-values go to positive infinity, the function's values go to negative infinity and as the x-values go to negative infinity, the function's values go to positive infinity.

It means,

$f(x)\rightarrow -\infty\text{ as }x\rightarrow \infty$

$f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty$

At x=0, the value of function is -3.

Note: All options are incorrect for end behavior.

From the given graph it is clear that the function is above the x-axis before -4 and after that it is below the x-axis. So,

$f(x)>0$ over the interval $(-\infty, -4).$

$f(x)$ over the interval $(-4,\infty).$

Therefore, the correct option is D.