The end behavior of a polynomial function is determined by the leading term, which is the term with the highest power of x. In this case, the leading term of the function f(x) = x³ – 2x² + 4x – 5 is x³.
As x approaches positive infinity (x → +∞), the leading term x³ also approaches positive infinity. This indicates that the function will rise to positive infinity on the right side of the graph.
Conversely, as x approaches negative infinity (x → -∞), the leading term x³ will approach negative infinity. Therefore, the function will drop down to negative infinity on the left side of the graph.
In summary, the end behavior of the function f(x) = x³ – 2x² + 4x – 5 is:
- As x → +∞, f(x) → +∞
- As x → -∞, f(x) → -∞