Question

What does the domain of a rational function represent?

a) All possible values of the function
b) Values that make the function undefined
c) Values that make the function equal to zero
d) Values that result in positive outputs

Answer 1

The domain of a rational function represents the values that make the function undefined. It consists of all real numbers except for the ones that cause the denominator to be zero.

Step-by-step explanation:

The domain of a rational function represents the values that make the function undefined.

A rational function is a function that can be written as a quotient of two polynomial functions. The domain of a rational function consists of all the real numbers except for the ones that cause the denominator to be zero. When the denominator is zero, the function becomes undefined. Therefore, the domain of a rational function is the set of all real numbers excluding the ones that make the denominator zero.

For example, consider the rational function f(x) = 1/(x-2). The domain of this function would be all real numbers except for x=2, because plugging in x=2 would cause the denominator (x-2) to be zero, resulting in an undefined value.