Questions: If the end behavior is decreasing to the left, what might be true about the function? Select all that apply. Select all that apply: The degree is even and the leading coefficient is positive. The degree is even and the leading coefficient is negative. The degree is odd and the leading coefficient is positive. The degree is odd and the leading coefficient is negative.

If the end behavior is decreasing to the left, what might be true about the function? Select all that apply.

Select all that apply:
The degree is even and the leading coefficient is positive.
The degree is even and the leading coefficient is negative.
The degree is odd and the leading coefficient is positive.
The degree is odd and the leading coefficient is negative.

Transcript text: If the end behavior is decreasing to the left, what might be true about the function? Select all that apply. Select all that apply: The degree is even and the leading coefficient is positive. The degree is even and the leading coefficient is negative. The degree is odd and the leading coefficient is positive. The degree is odd and the leading coefficient is negative.

Solution

Solution Steps

Step 1: Analyze the End Behavior of the Function

To determine the end behavior of a polynomial function, we need to consider the degree of the polynomial and the sign of the leading coefficient.

Step 2: Determine the Conditions for Decreasing Behavior to the Left

If a function decreases as it goes to the left (towards negative infinity), it suggests that the leading coefficient is negative.

Step 3: Consider the Degree of the Polynomial

If the degree is even, the function will have the same behavior in both directions. Therefore, for the function to decrease to the left, the leading coefficient must be negative.
If the degree is odd, the function will have opposite behaviors in each direction. For the function to decrease to the left, the leading coefficient must be negative.

Step 4: Evaluate the Given Options

Based on the analysis: