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When you graph a tangent function, the asymptotes represent x values 90 and 270.

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Q: What do the asymptotes represent when you graph the tangent function?
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Is it possible for graph of function to cross the horizontal assymptotes?

When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.


What are the rules of continuity of a graph?

If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".


How do you relate tangent graph with the math error in calculation of direction of resultant vector?

The tangent function will generate a calculator "math error" if the angle in questin is ±90 degrees. For these angles, the tangent function is not defined.


What is a tangent line?

Tangent line is a graph. This graph is to gather data.


How do you get the tangent line without the graph?

The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.