Asymptotes are important but can be a bit tricky when we try to understand how the tangent function looks on a graph.
Tough Vertical Asymptotes: The tangent function has vertical asymptotes at points like (x = \frac{\pi}{2} + n\pi). Here, (n) can be any whole number. This means that as you get closer to these points, the function gets really big (or goes to infinity). This makes it hard to understand what happens around these areas.
Breaks in the Graph: Because of these asymptotes, there are breaks in the graph. This makes it harder for students to see how the function acts when it nears these lines. It can be confusing to picture the behavior of the function.
Ideas to Help: Getting to know the unit circle can help you understand how the tangent function repeats itself and how it approaches the asymptotes. Working on practice problems about graphing can also make it easier to figure out these issues.
Asymptotes are important but can be a bit tricky when we try to understand how the tangent function looks on a graph.
Tough Vertical Asymptotes: The tangent function has vertical asymptotes at points like (x = \frac{\pi}{2} + n\pi). Here, (n) can be any whole number. This means that as you get closer to these points, the function gets really big (or goes to infinity). This makes it hard to understand what happens around these areas.
Breaks in the Graph: Because of these asymptotes, there are breaks in the graph. This makes it harder for students to see how the function acts when it nears these lines. It can be confusing to picture the behavior of the function.
Ideas to Help: Getting to know the unit circle can help you understand how the tangent function repeats itself and how it approaches the asymptotes. Working on practice problems about graphing can also make it easier to figure out these issues.