Which of the following functions exhibit the end behavior and ? Select all that apply.
Since the options are not provided, I cannot select the appropriate functions for end behavior.
I'm sorry, but you haven't provided a list of functions to choose from. Could you please provide the list of functions so that I can assist you further?
In order to determine the end behavior of a function, you need to analyze its degree and its leading coefficient. The end behavior of a function describes how the function behaves as the input values approach positive or negative infinity.
To determine the end behavior, follow these steps:
1. Identify the degree of the function. The degree is the highest power of the variable in the function. For example, a function of the form f(x) = ax^n has a degree of n.
2. Examine the leading coefficient. The leading coefficient is the coefficient of the term with the highest power. For example, in the function f(x) = ax^n, the leading coefficient is a.
Now you can determine the end behavior based on the degree and leading coefficient:
- If the degree is even (such as 2, 4, 6, etc.), and the leading coefficient is positive, the end behavior of the function is both up and down, meaning that the function approaches positive infinity as x approaches positive infinity and approaches negative infinity as x approaches negative infinity.
- If the degree is even and the leading coefficient is negative, the end behavior of the function is up and down, but flipped compared to the positive leading coefficient. In other words, the function approaches negative infinity as x approaches positive infinity and approaches positive infinity as x approaches negative infinity.
- If the degree is odd (such as 1, 3, 5, etc.), and the leading coefficient is positive, the end behavior of the function is up and down, similar to the even leading coefficient positive case.
- If the degree is odd and the leading coefficient is negative, the end behavior of the function is down and up, meaning that the function approaches negative infinity as x approaches positive infinity and approaches positive infinity as x approaches negative infinity.
Without knowing the specific functions provided as options, it is not possible to determine which functions exhibit the given end behavior. However, you can apply the above rules to determine the end behavior of specific functions in the options given.