Question

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

a.down on the left,
b.down on the right
c.down on the left,
d.up on the right up on the left,
e.up on the right up on the left,
f.down on the right

Answer 1

The end behavior of the function f(x) = -3x^38 + 7x^3 - 12x + 13 is that it goes down on both ends, meaning the graph will be down on the left and down on the right.

Step-by-step explanation:

To describe the end behavior of the polynomial function f(x) = −3x^{38} + 7x^3 − 12x + 13, we look at the leading term, which is the term with the highest power of x. In this case, the leading term is −3x^{38}. Since the coefficient is negative and the exponent is even, the end behavior is such that as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) also approaches negative infinity. Therefore, the graph of the polynomial will go down on both ends, or more specifically, down on the left and down on the right.