What is the end behaviour of the polynomial function h(x) = 2x^3 − 14x^2 − 36x? Explain.

Answer 1

The end behavior of a polynomial function can be determined by looking at the leading term of the polynomial. In this case, the leading term is 2x^3.

As x approaches positive infinity, the leading term 2x^3 becomes very large positive number, which means that the polynomial function h(x) will also become very large positive number. This means that the end behavior of h(x) as x approaches positive infinity is h(x) → +∞.

Similarly, as x approaches negative infinity, the leading term 2x^3 becomes very large negative number, which means that the polynomial function h(x) will also become very large negative number. This means that the end behavior of h(x) as x approaches negative infinity is h(x) → -∞.

In conclusion, the end behavior of the polynomial function h(x) = 2x^3 − 14x^2 − 36x is h(x) → +∞ as x → +∞ and h(x) → -∞ as x → -∞.