Answer:
Given the function: y= f(x) = [tex]x^3+2[/tex] ......[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) = [tex]x^3+2[/tex] 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) = [tex]0^3+2[/tex] = 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 [tex]x \rightarrow -\infty[/tex] then, [tex]f(x) \rightarrow -\infty[/tex] ,
as [tex]x \rightarrow +\infty[/tex] then, [tex]f(x) \rightarrow +\infty[/tex].
