Question

Which phrase describes the end behavior of the graph of ƒ(x) = –x5 – 4x4 + 7x2 – 2? up to the right, down to the left down to the right, up to the left up in both directions down in both directions

Answer 1

the highest degree is 5, an odd number, and the coefficient is -1, a negative number, so the graph extends downward to the right, upward to the left.

Answer 2

when highest degree is odd and leading coefficient is negative then the graph goes upward to the left and goes downward on the right

Explanation:

ƒ(x) = –x^5 – 4x^4 + 7x^2 – 2

given function has leading exponent 5. Highest degree is 5 that is an odd number.

the leading coefficient is -1 because we have -x^5

when highest degree is odd and leading coefficient is negative then the graph goes upward to the left and goes downward on the right