Answers:
Symmetry: about the origin
Extrema: No
End behavior: as x --> ∞, f(x) --> ∞ and as x --> -∞, f(x) --> -∞
Step-by-step explanation:
The graph for f(x) = x³ is
Then, we can see that the graph is symmetric over the origin becuase
f(-x) = -f(x)
(-x)³ = -(x³)
-x³ = -x³
On the other hand, it doesn't have an extreme value, there are no maximum or minimum points in a given interval.
Finally, we can see that when x increases, f(x) increases, and when x decreases f(x) decreases. So, the end behavior is
as x --> ∞, f(x) --> ∞
as x --> -∞, f(x) --> -∞