I'd be happy to help you with the questions regarding the polynomial function g(x) = -x^4 + 3x^2 - x - 1.
a. The zeros of the function are the values of x that make g(x) equal to zero. To find the zeros, you set g(x) = 0 and solve for x. In this case, the zeros are x = -1, 0, and 1.
b. The y-intercept is the point where the graph intersects the y-axis. To find it, you substitute x = 0 into the function and solve for y. In this case, the y-intercept is (0, -1).
c. The degree of the function is determined by the highest power of x in the polynomial. Since the highest power of x is 4, the degree of the function is even.
d. The leading coefficient is the coefficient of the term with the highest power of x. In this case, the leading coefficient is -1, which is negative.
e. The end behavior of the left end of the graph is determined by the leading term of the polynomial. Since the leading coefficient is negative and the degree is even, the graph will continue to go down on the left end.
f. The end behavior of the right end of the graph is also determined by the leading term of the polynomial. Since the leading coefficient is negative and the degree is even, the graph will continue to go down on the right end.
I hope this helps clarify the behavior and characteristics of the graph of the given polynomial function. If you have any more questions or need further explanation, feel free to ask!
