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: [tex]f(x)<0[/tex] over the interval [tex](-4,\infty).[/tex] (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,
[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow \infty[/tex]
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty[/tex]
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,
[tex]f(x)>0[/tex] over the interval [tex](-\infty, -4).[/tex]
[tex]f(x)<0[/tex] over the interval [tex](-4,\infty).[/tex]
Therefore, the correct option is D.
