Question

Which statement is true about the end behavior of the

graphed function?
(4-0.5,50
O As the x-values go to positive infinity, the function's values
go to positive infinity.
O As the x-values go to zero, the function's values go to
positive infinity.
the x-values go to negative infinity, the function's
values are equal to zero.
O As the x-values go to negative infinity, the function's
Values go to negative infinity
+20)
|(150)
(0.0)|​

Answer 1

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)<0` over the interval
`(-4,\infty).` (answer for question in image)

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)<0` over the interval
`(-4,\infty).`

Therefore, the correct option is D.