The end behavior of a polynomial is determined entirely by the leading term. For example, behaves the same way as
when
is very large in magnitude. All the problems in the picture are more or less the same. I'll pick out two examples:
1a) behaves like
.
will be positive regardless of the value of
, so to either the left or right, the graph of
will approach positive infinity or "rise" on both the left and right sides.
1c) has a leading term of
, so
behaves like
. When
, we have
, so that
. This means
rises to the left. If
, then
, so
falls to the right.
