#3 Choose the end behavior of the graph of the polynomial function.
f(x) -x(x-3)(5x+2), I think I have to foil to get -5x^3-2x^2+15x+6 So I think this one rises to the left and falls to the right. Please let me know if I did these correctly. Thanks
There is no = sign in your function definition. Is there a typing error?
The "end behavior" is determined by the sign of the x^3 term in this case.
To determine the end behavior of a polynomial function, you need to examine the leading term, which is the term with the highest exponent. In this case, the leading term is -5x^3.
The degree of the polynomial is determined by the exponent of the leading term, which is 3. Since the degree is odd, the graph will have opposite end behaviors in the left and right directions.
When the degree is odd and the leading coefficient is negative, like in this case, the graph will rise to the left and fall to the right.
Therefore, you are correct! The graph of the polynomial function f(x) = -5x^3 - 2x^2 + 15x + 6 will rise to the left and fall to the right.
Keep in mind that when you expanded the expression -x(x-3)(5x+2), you made a small error. The correct expansion should be -5x^3 + 17x^2 - 15x + 6.
So, in summary, the end behavior of the graph of the polynomial function f(x) = -5x^3 + 17x^2 - 15x + 6 is that it rises to the left and falls to the right.