Question

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

Answer 1

Here's the image of the answer!

Answer 2

Given the function: y= f(x) =
`x^3+2` ......[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) =
`x^3+2` 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) =
`0^3+2` = 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
`x \rightarrow -\infty` then,
`f(x) \rightarrow -\infty` ,

as
`x \rightarrow +\infty` then,
`f(x) \rightarrow +\infty`.