Question

Which statement correctly describes the end behavior of f(x)=−9x4+3x3+3x2−1?

As x→∞, f(x)→∞, and as x→−∞, f(x)→−∞.
As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.
As x→∞, f(x)→∞, and as x→−∞, f(x)→∞.
As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.

is it As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.

Answer 1

Think about the shape of an x^4 graph...
Now think about the shape of an -x^4 graph...
(hint: the x^4 looks a wee bit like a w... while the -x^4 looks a wee bit like a w reflected over the x-axis (so a flipped w)...
A regular w has both ends heading towards the sky (positive infinity)... while if you flip the w over (it becomes an m) and you see that both ends are now heading towards negative infinity!

Answer 2

No. the predominate term, x^4 is even, so it predominates at end.
x approaches +- inf, f(x) approaches negative inf

Answer 3

Nicely stated Bob : )

Answer 4

so would it be As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.