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What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
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.
The graph of the equation below is a hyperbola What are the slopes of the hyperbolas asymptotes?
7/12 and 7/12 is the answer
What is a sketch a graph?
Sketching a graph is drawing an approximation of the graph. The shape of the graph must be correct including the correct number of intercepts with the axes and any asymptotes. You are usually expected to label these. However, you are not required to ensure that the scales on the axes are accurate or other points on the graph are accurately marked.
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".
