Question

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.

Answer 1

The degree is odd, so the graph has ends that go in opposite directions. A negative coefficient means the graph rises on the left and falls on the right. Adding –x8 changes the degree to even, so the ends go in the same direction. Adding 5x7 changes the leading coefficient to positive, so the graph falls on the left and rises on the right.

Explanation:

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Answer 2

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.