What is the limit of the function?
lim f (x) = ∞ True or False
lim f (x) = -∞ True or False
I think its True and then False for the second statement
2. What is the end behavior of the function?
Enter your answer by filling in parentheses
As x→−∞ , f(x)→ ( )
As x→∞ , f(x)→ ( )
First one :
The first term 4x^8 will determine the limit at both ends [ its behavior will "overpower" the other terms ]
Note that when x = some large positive value = 4x^8 will be a large positive, i,e, the limit will be + inf
And....when x = some large negative =4x^8 will also be a large positive, i.e., the limit will also be + inf
So...you are correct !!!!
Again the highest power term -2x^5 will determine the end behavior
When x is a large negative -2(-x)^5 = will be positive
So as x approaches -inf, f(x) approaches infinity
On the other hand, when x is a large positive -2(x)^5 = will be negative
So as x approaches inf, f(x) approaches negative infinity
See the graph here : https://www.desmos.com/calculator/6swdftdxku