Consider the leading term of the polynomial function. What is the end behavior of the graph?
2x^7 – 8x^6 – 3x^5 – 3
(1 point)
Responses
The leading term is 2x7. Since n is odd and a is positive, the end behavior is up and up.
The leading term is 2x7. Since n is odd and a is positive, the end behavior is down and down.
The leading term is 2x7. Since n is odd and a is positive, the end behavior is down and up.
The leading term is 2x7. Since n is odd and a is positive, the end behavior is up and down.
The correct response is: The leading term is 2x^7. Since n is odd and a is positive, the end behavior is up and up.
The correct answer is: The leading term is 2x^7. Since the exponent (n) is odd and the coefficient (a) is positive, the end behavior is up and up.
To determine the end behavior of the graph of a polynomial function, look at the leading term of the function. In this case, the leading term is 2x^7.
The exponent of the leading term is 7, which is an odd number. If the exponent of the leading term is odd:
- If the coefficient (a) of the leading term is positive, then the end behavior is up and up.
- If the coefficient (a) of the leading term is negative, then the end behavior is down and down.
Since the coefficient of the leading term in the given polynomial function is positive, the end behavior is up and up.
Therefore, the correct response is:
The leading term is 2x^7. Since n is odd and a is positive, the end behavior is up and up.