What is the end behavior of the graph of the polynomial function y = 10x9 - 4x?
Solution:
To understand the end behavior of the polynomial function given in the problem statement the function’s graph needs to be plotted and is shown below.
The meaning of end behavior is how the function ‘y’ (in this case) moves when x tends towards both ∞ and - ∞.
From the above graph the following inferences can be drawn:
As x → ∞ y → ∞. This is apparent from the upward movement of the graph of the function y=10x9 –4x
As x →- ∞ y → -∞ This inference is also drawn from the above graph i.e. as x values become more negative the graph of y also travels towards infinity i.e. southward on the LHS of the above graph.
Even though the graph of the function remains flat in between x = -4 to x = 4. After these points, the graph moves towards infinity exponentially.
What is the end behavior of the graph of the polynomial function y = 10x9 - 4x?
Summary:
The end behavior of the graph of the polynomial function y = 10x9 - 4x is that it moves towards infinity in both directions as x moves towards infinity in both directions. Mathematically it means that as x → ∞ y → ∞ and As x → - ∞ y → -∞