Rational Functions Domain and Range Concept with Examples

#globalmathinstiute #anilkumarmath Rational Functions Domain and Range Concept with Examples
How to find domain and range of rational functions?
Understand with examples.
Rational functions are quotient of two polynomial functions where the denominator is not equal to zero. If for x = a, the denominator is zero then it will have a vertical asymptote of a have a vertical asymptote x = a or hole at x = a. Hole will exist only if we have a common factor in both numerator and denominator. Graph of these functions can have horizontal asymptote for the following conditions:
1. If degree of denominator is higher the y = 0 is the horizontal asymptote
2. If degree of both numerator and denominator is same then y = a/b is the horizontal asymptote where a and b are respective the leading coefficients of numerator and denominator.
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[blackzetsu]

Explain how did you restricted the range or y with 0?

[sunilkjha]

sir what will be the double modulous of x ||x||

[RamMohan-wyqj]

Hello Sir.Can you help me how to calculate range for