The end behaviour of a function refers to the behavior of the function as the input values get extremely large or extremely small. It describes how the function approaches its highest or lowest values as the input values approach positive or negative infinity.
To determine the end behaviour of a function, we can look at the highest degree term in the function's equation. If the highest degree term is an even power, the end behaviour will be the same on both sides of the graph. If the highest degree term is an odd power, the end behaviour will be different on each side of the graph.
The two types of end behaviour for functions are horizontal and vertical. Horizontal end behaviour occurs when the function approaches a constant value as the input values get extremely large or small. Vertical end behaviour occurs when the function approaches positive or negative infinity as the input values get extremely large or small.
Yes, a function can have both horizontal and vertical end behaviour. This occurs when the function has a highest degree term with an odd power and a constant term. As the input values approach positive or negative infinity, the function will approach a constant value on one side and positive or negative infinity on the other side.
The end behaviour of a function can give us information about the overall shape of the function's graph. It can help us determine if the function has a horizontal or vertical asymptote, and if the graph will have a positive or negative slope on each side. This information can also help us sketch the graph of a function without having to plot many points.
