Question

1. In a certain function c(x), as x approaches negative and positive infinity, the function approaches positive infinity. What is the sign of the leading coefficient? Is the degree of the function even or odd?

a. negative, even
b. positive, even
c. negative, odd
d. positive, odd

Answer 1

The sign of the leading coefficient is positive, and the degree of the function must be even because the function approaches positive infinity as x approaches both negative and positive infinity.

Step-by-step explanation:

The student has asked about the properties of a function c(x) where as x approaches both negative and positive infinity, c(x) approaches positive infinity. To determine the sign of the leading coefficient and the degree of the function, we consider the end-behavior of the function.

For a polynomial function, if both ends go off to positive infinity, the leading coefficient must be positive. Additionally, this behavior is indicative of an even degree polynomial since odd degree polynomials have opposite end behaviors (as x goes to positive infinity, an odd-degree polynomial will go to positive or negative infinity, and as x goes to negative infinity, it will go in the opposite direction).

Therefore, the correct answer is: b. positive, even.