F(x)= -x^3 + 1

Describe the right-hand and left-hand behavior of the graph of the polynomial function. (Select all that apply.)

h(x) = 1 − x6

...The graph rises to the right.

...The graph falls to the right.

...The graph rises to the left.

...The graph falls to the left.

h(x) = 1 − x6

...The graph rises to the right.

...The graph falls to the right.

...The graph rises to the left.

...The graph falls to the left.

Because the exponent is even, the function is even. This means there is an axis of symmetry at x=0 about which the graph is reflected.

The curve itself goes through the point (1,1), but rapidly heads off toward positive infinity when x>1, and rapidly heads toward 0 when x<1. The same is true on the left side of x=0. For x<-1, the value of F(x) is very large very fast; for x>-1, the value of F(x) is very near zero.

The curve includes the points (0,0) and (-1,1).

For x = ±.999, F(x) ≈ .000045

For x = ±1.001, F(x) ≈ 22,000

The curve itself goes through the point (1,1), but rapidly heads off toward positive infinity when x>1, and rapidly heads toward 0 when x<1. The same is true on the left side of x=0. For x<-1, the value of F(x) is very large very fast; for x>-1, the value of F(x) is very near zero.

The curve includes the points (0,0) and (-1,1).

For x = ±.999, F(x) ≈ .000045

For x = ±1.001, F(x) ≈ 22,000