Verified answer

f(x)=-x^4-4.

The graph of f(x)=x^4 is a parabola, and because the term x^4 is negative, the parabola opens downward.

The -4 term at the end of the function tells us that the graph is shifted down 4 units. So it's a parabola that opens down, with a vertex of (0,-4).

The end behavior is even, and both ends point down, or decrease without bound.

I plugged the function into wolfram to double check. http://www.wolframalpha.com/input/?i=-x4-4

If you need to show more work than that:

You just need the y-intercept since the function doesn't cross the x-axis.

Intercept: f(x)=y=0^4-4

y=-4.

(0,-4).

Get some other values to help with graphing now.

y=-(1)^4-4

y=-1-4

y=-5.

(1,-5).

y=-(-1)^4-4

y=-1-4

y=-5.

(-1,-5).

y=-(2)^4-4

y=-16-4

y=-20.

(2,-20).

y=-(-2)^4-4

y=-16-4

y=-20.

(-2,-20).