x^5 is an odd power
so, as x -> +∞, f(x) -> +∞
as x -> -∞, f(x) -> -∞
-3x5 + 9x4 + 5x3 + 3
how would I solve this?
so, as x -> +∞, f(x) -> +∞
as x -> -∞, f(x) -> -∞
In the given polynomial function, the leading term is -3x^5.
To understand the end behavior, you need to consider the sign of the leading coefficient (-3) and the degree of the leading term (5).
Here are the rules:
- If the leading coefficient is positive, the graph will rise on both ends.
- If the leading coefficient is negative, the graph will fall on both ends.
- If the degree of the leading term is odd, the graph will approach different quadrants on the left and right sides as x approaches positive or negative infinity.
- If the degree of the leading term is even, the graph will approach the same quadrant on both sides as x approaches positive or negative infinity.
In the given polynomial, the leading coefficient is negative (-3), and the degree of the leading term is odd (5). Therefore, the end behavior is as follows:
- As x approaches positive infinity, the graph will fall towards the negative y-axis.
- As x approaches negative infinity, the graph will rise away from the negative y-axis.
In summary, the end behavior of the graph is a falling curve on both ends. The leading term is -3x^5.