Choose the end behavior of the graph of each polynomial function.

A f(x)= -5x^3-4x^2+8x+5
B f(x)= -4x^6+6x^4-6x^3-2x^2
C f(x)= 2x(x-1)^2(x+3)

A= falls to the left and rises to the right
B= Falls to the left and right
C=Rises to the right and left.

Got it thanks

disagree on the first one

-x^3 = -x (x)^2
x^2 is always +
-x is positive left and negative right
rises to left, falls to right

To determine the end behavior of each polynomial function, we look at the leading term of the polynomial.

In polynomial function A, the leading term is -5x^3. Since the exponent of the leading term is odd, the graph falls to the left as x approaches negative infinity and rises to the right as x approaches positive infinity. Therefore, the correct answer for A is "falls to the left and rises to the right."

In polynomial function B, the leading term is -4x^6. Again, since the exponent of the leading term is even, the graph falls to the left and right as x approaches negative and positive infinity. Therefore, the correct answer for B is "falls to the left and right."

In polynomial function C, the leading term is 2x(x-1)^2(x+3). As x approaches negative infinity, the leading term becomes negative, causing the graph to rise to the left. As x approaches positive infinity, the leading term becomes positive, causing the graph to rise to the right. Therefore, the correct answer for C is "rises to the right and left."

So, the correct choices for the end behavior of the graphs are:

A: Falls to the left and rises to the right.
B: Falls to the left and right.
C: Rises to the right and left.

To determine the end behavior of a polynomial function, we need to consider the degree of the function and the sign of the coefficient of the leading term.

A) The degree of the polynomial function f(x) = -5x^3 - 4x^2 + 8x + 5 is 3. Since the degree is odd, the end behavior will be opposite on the left and right sides. The leading term is -5x^3, so the coefficient is negative. Hence, the end behavior of this function is falls to the left (as x approaches negative infinity) and rises to the right (as x approaches positive infinity).

B) The degree of the polynomial function f(x) = -4x^6 + 6x^4 - 6x^3 - 2x^2 is 6. Since the degree is even, the end behavior will be the same on both the left and right sides. The leading term is -4x^6, so the coefficient is negative. Therefore, the end behavior of this function is falls to the left (as x approaches negative infinity) and falls to the right (as x approaches positive infinity).

C) The degree of the polynomial function f(x) = 2x(x-1)^2(x+3) is not explicitly given, but by expanding and simplifying the function, we can determine that its degree is 4. Since the degree is even, the end behavior will be the same on both the left and right sides. However, instead of looking at the leading term's coefficient, we need to analyze the signs of the factors. The expression (x-1)^2 is always non-negative, and since it multiplies with a positive coefficient of 2x(x+3), the end behavior of this function is rises to the left (as x approaches negative infinity) and rises to the right (as x approaches positive infinity).

So, the correct answers are:
A) f(x) falls to the left and rises to the right
B) f(x) falls to the left and falls to the right
C) f(x) rises to the left and rises to the right