Without using technology, describe the end behavior of f(x) = −3x38 + 7x3 − 12x + 13.

down on the left, down on the right

down on the left, up on the right

up on the left, down on the right

up on the left, up on the right

Second option: down on the left, down on the right.

Clearly when x is bigger than one the term -x^38 will dominate the result.

When absolute value of x grows, x^38 becomes a larger positive number and - x^38 a larger negative number. Then both ends of the function tend to negative infinity.