Question

For the polynomial

f(x) = 2x^3 – 9x^2 +11x – 20,
as x → -infinity, f(x) → infinity.

1.True
2.False

Answer 1

The statement "As x → -infinity, f(x) → infinity" is false for the polynomial f(x) = 2x^3 − 9x^2 +11x − 20. The correct behavior is that f(x) approaches negative infinity as x approaches negative infinity because the leading term with a positive coefficient dominates the polynomial's behavior.

Step-by-step explanation:

For the polynomial f(x) = 2x^3 − 9x^2 +11x − 20, we need to determine the behavior of f(x) as x approaches negative infinity.

As x approaches negative infinity in a cubic polynomial where the leading coefficient is positive, the value of f(x) actually approaches negative infinity, not positive infinity. So, the statement "As x → -infinity, f(x) → infinity" is False. The correct behavior is the opposite: As x approaches negative infinity, f(x) approaches negative infinity because the leading term, 2x^3, dominates the behavior of the polynomial at extreme values of x, and since it's a positive coefficient with an odd power, the graph will descend into negative infinity.