A limit on a graph is a value that a function approaches as the input (x-value) approaches a certain number. It can be thought of as the value that the function "gets closer and closer to" as the input approaches a specific value.
To find the limit of a function from a graph, you can either use the direct substitution method or the graphing calculator method. For the direct substitution method, simply plug in the value that the input is approaching and evaluate the function. For the graphing calculator method, zoom in on the point where the input is approaching and see what value the function is approaching.
An asymptote on a graph is a line that a function approaches but never touches or crosses. It can be a horizontal, vertical, or slant asymptote and indicates where the function has a limit of positive or negative infinity.
To determine if a graph has a horizontal asymptote, you can use the limit definition of an asymptote. Take the limit of the function as x approaches positive or negative infinity. If the limit is a finite number, then there is no horizontal asymptote. If the limit is positive or negative infinity, then there is a horizontal asymptote at that value.
Yes, a graph can have more than one asymptote. It can have multiple horizontal, vertical, or slant asymptotes depending on the behavior of the function at different points on the graph. It is also possible for a graph to have no asymptotes.