The addition of either - x8 or 5x7 will change the end behavior of y = - 2x7 + 5x6 - 24.

Explain how each of the added terms above would change the graph.

The addition of a - x^8 term will change the end behavior of the graph because the degree of the polynomial becomes even rather than odd. While the - 2x^7 has an end behavior in which the graph goes toward infinity on the - x side and to negative infinity on the positive x side, the addition of a - x^8 will make both ends of the group ( + and - x sides) go toward negative infinity. If you add a 5x^7 term instead, the largest degree term in the polynomial is now 3x^7. Since this leading term is now positive rather than negative, the end behavior will flip compared to the original polynomial, making the graph go toward negative infinity on the - x side and positive infinity on the + x side.