Describe the end behavior of the graph of the polynomial function. Then evaluate the function for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. Then graph the function. Number one: y=x^4-2x^2-x-1

Check the constant(-1) in your Eq and

make sure it is correct.
(X,Y)
(-4,227)
(-3,65)
(-2,9)
(-1,-1)
(0,-1)
(1,-3)
(2,5)
(3,59)
(4,219)

To describe the end behavior of a graph of a polynomial function, we need to look at the degrees of the terms in the polynomial.

For the polynomial function y = x^4 - 2x^2 - x - 1, we can see that the highest power of x is 4. Therefore, we say that the degree of this polynomial is 4.

When the degree is even and the leading coefficient (the coefficient of the term with the highest power) is positive, the graph of the polynomial will have the following end behaviors:

- As x approaches negative infinity, y approaches positive infinity.
- As x approaches positive infinity, y approaches positive infinity.

Now let's evaluate the function for various values of x to understand how the graph behaves:

For x = -4:
y = (-4)^4 - 2(-4)^2 - (-4) - 1
= 256 - 32 - (-4) - 1
= 256 - 32 + 4 - 1
= 227

For x = -3:
y = (-3)^4 - 2(-3)^2 - (-3) - 1
= 81 - 18 - (-3) - 1
= 81 - 18 + 3 - 1
= 65

For x = -2:
y = (-2)^4 - 2(-2)^2 - (-2) - 1
= 16 - 8 - (-2) - 1
= 16 - 8 + 2 - 1
= 9

For x = -1:
y = (-1)^4 - 2(-1)^2 - (-1) - 1
= 1 - 2 - (-1) - 1
= 1 - 2 + 1 - 1
= -1

For x = 0:
y = (0)^4 - 2(0)^2 - (0) - 1
= 0 - 0 - 0 - 1
= -1

For x = 1:
y = (1)^4 - 2(1)^2 - (1) - 1
= 1 - 2 - 1 - 1
= -2

For x = 2:
y = (2)^4 - 2(2)^2 - (2) - 1
= 16 - 8 - 2 - 1
= 5

For x = 3:
y = (3)^4 - 2(3)^2 - (3) - 1
= 81 - 18 - 3 - 1
= 59

For x = 4:
y = (4)^4 - 2(4)^2 - (4) - 1
= 256 - 32 - 4 - 1
= 219

Now, let's graph the function:

To graph the function y = x^4 - 2x^2 - x - 1, plot the points we just found and connect them smoothly with a curve.