Select the graph and the description of the end behavior of f(x) = x3 + 2.

Given the function: y= f(x) =           ......[1]

End behavior of a polynomial function is the behavior of the graph of function  f(x) as x approaches positive infinity or negative infinity.

Also, the degree and the leading coefficient of a polynomial function determine the end behavior of the function.

Since the given function  f(x) =  is cubic function with degree 3  and leading coefficient 1 (i.e positive).

y-intercept of the function:

Substitute the value x= 0 in [1] to solve for y;

y= f(x) = = 0+2 =2

Therefore, the y-intercept of the function is 2 (which means the graph cut the y-axis at 2 i.e, y=2)

Since, the  degree of the function is odd and the leading coefficient is positive.  

so, the end behavior is;

as   then, ,

as then, .