The end behavior of a polynomial function refers to the behavior of the graph as the variable x approaches positive or negative infinity.
Now, let’s analyze the polynomial function given: y = 10x9 – 4x.
This polynomial is of degree 9, which is determined by the highest power of x, that is, x9. The coefficient of the leading term (10 in this case) also plays a key role in determining the end behavior.
Since the degree (9) is odd and the leading coefficient (10) is positive, we can conclude the following:
- As x approaches positive infinity (x → +∞), y will also approach positive infinity (y → +∞).
- As x approaches negative infinity (x → -∞), y will approach negative infinity (y → -∞).
Therefore, the end behavior of the graph of the polynomial function y = 10x9 – 4x shows that the graph rises to the right and falls to the left.