Domain Of A Graph With Asymptotes
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A reciprocal function a special case of a rational function cannot have values in its domain that cause the denominator to equal zero.
Domain of a graph with asymptotes. The function f x a x a 0 has the same domain range and asymptotes as f x 1 x. Use the domain of a rational function to define vertical asymptotes. A reciprocal function cannot have values in its domain that cause the denominator to equal zero.
The vertical asymptote of the function is x b and the horizontal asymptote is y c. A vertical asymptote represents a value at which a rational function is undefined so that value is not in the domain of the function. The vertical and horizontal asymptotes help us to find the domain and range of the function.
Now the graph of the function f x a x b c a 0 is a hyperbola symmetric about the point b c. Here is our graph with the vertical and horizontal asymptotes plotted as dashed lines.
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