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, .

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.