Question

Which of the following Best describes the function -x^4+1

a)The degree of the function is even so the ends of the graph continue in opposite directions. Because the leading coefficient is positive the left side of the graph continues down the coordinate plane and the right side continues upward.
b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward
c) The degree of the function is even so the ends of the graph continue in opposite directions. because the leading coefficient is negative the left side of the graph continues up the coordinate plane and the right side continues downward
d) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is positive the left side of the graph continues of the coordinate plane and the right side also continues upward.

Answer 1

b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward

Step-by-step explanation

The given polynomial function is

`f(x) = - {x}^(4) + 1`

The degree of this function is even which is 4.

The function extends in the same direction at both ends.

In other words both ends continue in the same direction.

Since the coefficient of the leading term is negative, the graph extends to negative infinity at both ends.

The correct answer is B