No vertical Asymptote
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A vertical asymptote is a vertical line on a graph at which the function’s value is undefined or approaches infinity or negative infinity. Therefore, if a function has no vertical asymptotes, it means that it is continuous and well-defined at all points along the vertical axis.
Function without vertical asymptotes could be any function that doesn’t have any vertical discontinuity or singularities. Some examples of such functions are:
1. Linear Functions: A linear function such as y = mx + b doesn’t have any vertical asymptote since it’s defined for all values of x.
2. Polynomial Functions: A polynomial function such as y = x^3 + 2x^2 – x + 1 doesn’t have any vertical asymptote since it’s defined for all values of x.
3. Trigonometric Functions: The sine, cosine, and tangent functions are continuous functions, which means they don’t have any vertical asymptotes.
4. Exponential and Logarithmic Functions: Exponential and logarithmic functions such as y = e^x and y = ln(x) don’t have any vertical asymptotes since they are defined for all positive real numbers.
To conclude, any function that is continuous and well-defined for all values of x will not have any vertical asymptotes.
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