Question

End behavior of polynomials I give 20 points

Answer 1

It fallsto the right because the behavior of polynomials is effected by the x and exponents

Answer 2

The end behavior of a polynomial is determined entirely by the leading term. For example,
`2x^4-x+1` behaves the same way as
`2x^4` when
`x` is very large in magnitude. All the problems in the picture are more or less the same. I'll pick out two examples:

1a)
`f(x)=5x^6-3x^3-4x^2+8x` behaves like
`5x^6`.
`x^6` will be positive regardless of the value of
`x`, so to either the left or right, the graph of
`f(x)` will approach positive infinity or "rise" on both the left and right sides.

1c)
`f(x)=-4x(x-4)(x+2)` has a leading term of
`-4x^3`, so
`f(x)` behaves like
`-4x^3`. When
`x<0`, we have
`x^3<0`, so that
`-4x^3>0`. This means
`f(x)` rises to the left. If
`x>0`, then
`-4x^3<0`, so
`f(x)` falls to the right.