Step-by-step explanation:
To find the zeros of the function, we set f(x) = 0 and solve for x:
x^3 + 2x^2 - 5x - 6 = 0
By inspection, x = 1 is a root of the function (since f(1) = 0), so we can factor out (x - 1) from the function:
(x - 1)(x^2 + 3x + 6) = 0
To find the remaining zeros, we can solve the quadratic equation x^2 + 3x + 6 = 0 using the quadratic formula or by completing the square. However, since the discriminant of the quadratic equation is negative, the quadratic equation has no real roots. Therefore, the zeros of the function are x = 1.
The end behavior of the function's graph can be determined by looking at the degrees of the terms in the function:
- The highest power of x in the function is x^3, with a positive coefficient. This means that as x approaches positive infinity, the function will also approach positive infinity.
- The end behavior as x approaches negative infinity is the same as when x approaches positive infinity, as the function has an odd degree.
Therefore, the correct end behavior of the function's graph is that as x approaches positive or negative infinity, the function approaches positive infinity.
