Consider the leading term of the polynomial function. What is the end behavior of the graph?
2x^7-8x^6-3x^5-3
The leading term of the polynomial function is 2x^7.
The end behavior of the graph can be determined by looking at the sign of the leading coefficient (2) and the degree of the polynomial (7).
Since the degree is odd and the leading coefficient is positive, the end behavior of the graph will be as follows:
- As x approaches negative infinity, the graph will also approach negative infinity.
- As x approaches positive infinity, the graph will also approach positive infinity.
To determine the end behavior of the graph of a polynomial function, you need to look at the leading term of the polynomial. The leading term is the term with the highest exponent.
In the given polynomial, the leading term is 2x^7. The exponent of this term is 7, which means the degree of the polynomial is 7. The degree of the polynomial is the highest power of x in the polynomial.
In general, for a polynomial of odd degree (such as degree 7 in this case), the end behavior of the graph is as follows:
- As x approaches negative infinity (-∞), the function value (y) also approaches negative infinity (-∞).
- As x approaches positive infinity (+∞), the function value (y) also approaches positive infinity (+∞).
Therefore, the end behavior of the graph of the given polynomial function is as follows:
- As x approaches negative infinity (-∞), the graph of the function goes down.
- As x approaches positive infinity (+∞), the graph of the function goes up.
Note that this analysis is based on the leading term and the degree of the polynomial. Other terms in the polynomial equation do not affect the end behavior in this case.