Question

Consider the function f(x) = -2x7 - 6x3 - x + 5 The end behavior is:

a) As x --> [infinity] , y --> [infinity] As x --> -[infinity] , y --> -[infinity]
b) As x --> [infinity] , y --> -[infinity] As x --> -[infinity] , y --> -[infinity]
c) As x --> [infinity] , y --> [infinity] As x --> -[infinity] , y --> [infinity]
d) As x --> [infinity] , y --> -[infinity] As x --> -[infinity] , y --> [infinity]

Answer 1

The end behavior of a function with a leading term of -2x^7 is as x approaches positive infinity, y approaches negative infinity and as x approaches negative infinity, y approaches negative infinity.

Step-by-step explanation:

The end behavior of a function can be determined by examining the leading term of the function. In this case, the leading term of the function f(x) = -2x^7 is -2x^7. Since the exponent of the leading term is odd and the coefficient is negative, the end behavior is as follows:

1. As x approaches positive infinity, y approaches negative infinity.
2. As x approaches negative infinity, y approaches negative infinity.

Therefore, the correct answer is (b) As x --> [infinity], y --> -[infinity] As x --> -[infinity], y --> -[infinity].