The end behavior of a polynomial function refers to how the graph behaves as the input (or ‘x’ value) approaches positive and negative infinity. For the polynomial function y = 10x9 – 4x, we can analyze its end behavior by considering the leading term, which is the term with the highest power of ‘x’. In this case, the leading term is 10x9.
Since the degree of the leading term (9) is odd and the leading coefficient (10) is positive, we can summarize the end behavior as follows:
- As x approaches positive infinity (x → +∞), y also approaches positive infinity (y → +∞). This means that the graph will rise to the right.
- As x approaches negative infinity (x → -∞), y approaches negative infinity (y → -∞). This indicates that the graph will fall to the left.
To visualize this, you can imagine the graph starting from the bottom left quadrant and rising up to the upper right quadrant as it moves from left to right across the coordinate plane.
In conclusion, the end behavior of the polynomial function y = 10x9 – 4x can be summarized as:
- As x → +∞, y → +∞
- As x → -∞, y → -∞