Question

Consider the function ƒ(x) = –x4 + 9. Determine which of the following is its graph, based on end behavior.

Answer 1

Explanation:

If the degree of the polynomial is even (positive) ends of the function will either upwards or downwards on axis.

If the coefficient of the leading term of a polynomial is negative, both the ends of the graph will move downwards.

The given function is,

f(x) = -x⁴ + 9

Degree of the polynomial = 4

Coefficient of the leading term = -1

Therefore, ends of the polynomial will open downwards.