Question
the end behavior of the graph of y=-4x^5-8x^3+4x+8
Answers
GPT 3.5
To determine the end behavior of the graph of the equation y = -4x^5 - 8x^3 + 4x + 8, we need to examine the leading term of the polynomial.
The leading term is the term with the highest degree, which in this case is -4x^5.
As x approaches negative infinity (x → -∞), the value of -4x^5 becomes increasingly negative, because an odd power of a negative number gives a negative result. Therefore, the graph approaches negative infinity as x goes to negative infinity.
As x approaches positive infinity (x → +∞), the value of -4x^5 becomes increasingly positive, because an odd power of a positive number gives a positive result. Therefore, the graph approaches positive infinity as x goes to positive infinity.
In summary, the end behavior of the graph is:
- As x approaches negative infinity (x → -∞), y approaches negative infinity.
- As x approaches positive infinity (x → +∞), y approaches positive infinity.
The leading term is the term with the highest degree, which in this case is -4x^5.
As x approaches negative infinity (x → -∞), the value of -4x^5 becomes increasingly negative, because an odd power of a negative number gives a negative result. Therefore, the graph approaches negative infinity as x goes to negative infinity.
As x approaches positive infinity (x → +∞), the value of -4x^5 becomes increasingly positive, because an odd power of a positive number gives a positive result. Therefore, the graph approaches positive infinity as x goes to positive infinity.
In summary, the end behavior of the graph is:
- As x approaches negative infinity (x → -∞), y approaches negative infinity.
- As x approaches positive infinity (x → +∞), y approaches positive infinity.