Consider the leading term of the polynomial function. What is the end behavior of the graph? 6x7 (1 point) Responses since n is odd and a is positive, the end behavior is down and up. since n is odd and a is positive, the end behavior is down and up. since n is odd and a is positive, the end behavior is up and up. since n is odd and a is positive, the end behavior is up and up. since n is odd and a is positive, the end behavior is up and down. since n is odd and a is positive, the end behavior is up and down. since n is odd and a is positive, the end behavior is down and down.
The "leading term" of a polynomial function is the term that contains the highest power of the variable, which determines the end behavior of the graph as the variable approaches positive and negative infinity. For the polynomial function given (6x^7), the leading term is 6x^7. Here, n (the degree of the polynomial) is 7, which is odd, and a (the leading coefficient) is 6, which is positive.
For polynomial functions with an odd degree and a positive leading coefficient:
- As x approaches positive infinity (+∞), the function f(x) also approaches positive infinity.
- As x approaches negative infinity (−∞), the function f(x) approaches negative infinity.
Hence, since n is odd and a is positive, the end behavior of the graph for the given polynomial function 6x^7 is:
down (as x → −∞) and up (as x → +∞).
This is a standard end-behavior for polynomial functions with odd degrees and positive leading coefficients. Your response should match this description, but in the options you provided, there are repetitions. The correct answer is:
"since n is odd and a is positive, the end behavior is down and up."