Question

. Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3

Answer 1

As x-> -∞, y->∞

x-> ∞, y->-∞

Leading term -3x^5

Explanation:

`-3x^5 + 9x^4 + 5x^3 + 3`

Leading term is the first term of the polynomial

Leading term -3x^5

The exponent of leading term is 5 that is odd

and the coefficient of leading term is -3 that is negative

When the coefficient of leading term is negative and exponent of leading term is odd then the graph goes up on the left and goes down on the right.

As x-> -∞, y->∞

x-> ∞, y->-∞

Leading term -3x^5

Answer 2

we are given the polynomial function -3x5 + 9x4 + 5x3 + 3 and is asked in the problem to determine the end behavior of the graph. Since the highest degree of the function is 5, then it is expected that there are 4 extremes that can be seen from the graph. This can be at minima or maxima.