Final answer:
A horizontal asymptote of a graph is a horizontal line that the graph approaches but never touches as x tends to positive or negative infinity.
Step-by-step explanation:
An asymptote is a line that a graph approaches but never touches. In the case of a horizontal asymptote, it is a horizontal line that the graph approaches as x tends to positive or negative infinity.
When we say that y=b is a horizontal asymptote of y=f(x), it means that as x gets very large or very small, the values of f(x) get closer and closer to the value b. The graph will never cross the horizontal line y=b.
For example, if we have y=f(x) = 2x + 5 and y=b=3, then as x becomes very large or very small, the values of f(x) will approach 3 but never actually reach it. The graph will get closer and closer to the horizontal line y=3.