Question

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

Answer 1

F(x)=x^3+2
we see the power is odd
the ends go in opsoite directions
we know that if the leadind coefient (number in front of highest power term) is positive, then odd powered polynomials go from bottom left to top right
and for even ones, it goes both up

for negative, odd ones go from top left to bottom right
for even, both go down

we gots
f(x)=1x^3+2
positive and odd, so it goes from bottom left to top right

as x approaches negative inifnity, y approaches negaitve infinity
as x approaches infinity, y approaches infinity

Answer 2

Answer:

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, $f(x) \rightarrow +\infty$.