Find the correct end behavior for a given polynomial function.
3.36x^4+8x^2+x-9
End behavior is determined by whether the first number is positive or negative, and if the degree is even or odd. Since the leading coefficient is positive and the degree is even, the end behavior is (up, up) (by 'up' I mean an arrow pointing up)
To find the correct end behavior of a polynomial function, we need to examine the highest degree term. In this case, the highest degree term is 3.36x^4.
The degree of the term tells us about the shape of the graph and the behavior of the function as x approaches positive and negative infinity.
For a polynomial function of even degree with a positive leading coefficient (in this case, 3.36), the end behavior is as follows:
- As x approaches positive infinity, the function values (y-values) also approach positive infinity.
- As x approaches negative infinity, the function values (y-values) also approach positive infinity.
So, the correct end behavior for the given polynomial function, 3.36x^4 + 8x^2 + x - 9, is:
- As x approaches positive infinity, the function values approach positive infinity.
- As x approaches negative infinity, the function values approach positive infinity.