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 $x$, we have $x^3$, so that $-4x^3>0$. This means $f(x)$ rises to the left. If $x>0$, then $-4x^3$, so $f(x)$ falls to the right.