How to find the range of a quadratic rational function algebraically?
Answers
he domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
A rational function is a function of the form f(x)=p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .
The domain of a rational function consists of all the real numbers x except those for which the denominator is 0 . To find these x values to be excluded from the domain of a rational function, equate the denominator to zero and solve for x .
For example, the domain of the parent function f(x)=1x is the set of all real numbers except x=0 . Or the domain of the functionf(x)=1x−4 is the set of all real numbers except x=4 .
Now, consider the function f(x)=(x+1)(x−2)(x−2) . On simplification, when x≠2 it becomes a linear function f(x)=x+1 . But the original function is not defined at x=2 . This leaves the graph with a hole when x=2 .