What is the end behavior of the function f(x) = x³ + 2x² + 4x + 5?

Solution:

End behaviour of a function is the nature of the value as the function argument approaches + ∞ and - ∞.

The end behaviour of a polynomial function is determined by the term of highest degree.

Given, f(x) = x³ + 2x² + 4x + 5

The end behaviour is determined by x³.

Hence, f(x) → +∞ as x → +∞ and f(x) → -∞ as x → -∞

For large values of x, the term of highest degree will be much larger than the other terms, which can effectively be ignored.

The coefficient of x³ is positive and its degree is odd.

Therefore, the end behaviour is f(x) → +∞ as x → +∞ and f(x) → -∞ as x → -∞

What is the end behavior of the function f(x) = x³ + 2x² + 4x + 5?

Summary:

The end behavior of the function f(x) = x³ + 2x² + 4x + 5 is f(x) → +∞ as x → +∞ and f(x) → -∞ as x → -∞.