The function h(x) = ₋x³₊4x²₊x₋3 is the function which have the same end behavior as p(x) which has a degree 3 polynomial with a negative leading coefficient.
Given, p(x) is a degree 3 polynomial with a negative leading coefficient .
To find the end behavior we need to determine the highest degree, leading term and leading coefficient.
If the function is in general form, the first variable's power, which is the highest power of the variable that appears in the polynomial, is the degree of the polynomial. The phrase with the most powerful variable—also known as the term with the highest degree—is the leading term. The coefficient of the leading term is known as the leading coefficient.
A. h(x) = ₋x⁵ ₊ 4x, here there is no degree 3 and also there is no negative leading coefficient. Hence option A doesn't match to p(x).
B. h(x) = x³ ₊ 2x, here the degree is 3 but no negative leading coefficient. Hence option B doesn't match to p(x).
C. h(x) = ₋x⁶ ₊ 7x³ ₊ 1, here there is negative leading coefficient but the degree is not 3. Hence option C doesn't match to p(x).
D. h(x) = x + 3x³ - 4x + 2, here there is no negative leading coefficient. Hence option D doesn't match to p(x).
E. h(x) = x⁵-x³ +8, here the highest degree is not 3. Hence option E doesn't match to p(x).
F. h(x) = -x³+4x²+x - 3, here we have the highest degree as 3 and it's leading term is ₋x³ and it's leading coefficient is ₋1. Hence option F matches function p(x).
therefore we get the function which have the same end behavior as p(x) as h(x) = ₋x³ ₊ 4x² ₊ x ₋ 3.
Learn more about Algebra here:
brainly.com/question/855307
#SPJ9
