Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x5 + 9x4 + 5x3 + 3
how would I solve this?
the lead term is -3x^5 , which on the graph would drop down rapidly into the fourth quadrant when x gets larger.
The diameter of a circle is 24 feet. Using the formula A = r2, what is the area of the circle? Use 3.14 for pi.
ft2
To analyze the end behavior of a polynomial function, you need to examine the leading term. The leading term is the term with the highest degree or the term that has the largest exponent.
In the given polynomial function, the leading term is -3x^5, which has a degree of 5.
To determine the end behavior:
1. If the degree is odd (e.g., 1, 3, 5), the end behavior will be opposite. For example, if the leading term is positive, then the end behavior will be negative as x approaches negative infinity, and positive as x approaches positive infinity.
2. If the degree is even (e.g., 2, 4, 6), the end behavior will be the same. For example, if the leading term is positive, then the end behavior will also be positive as x approaches both negative and positive infinity.
In this case, the degree is odd (5), and the leading term, -3x^5, has a coefficient of -3. Therefore, as x approaches negative infinity, the end behavior will be negative, and as x approaches positive infinity, the end behavior will be positive.
The end behavior can be summarized as:
As x approaches negative infinity, the graph decreases.
As x approaches positive infinity, the graph increases.
To determine the end behavior, you only need to consider the sign of the leading term's coefficient (in this case, -3) and the degree of the leading term (in this case, the leading term is of degree 5).