greg1313 said:1. All the values a function assumes over its domain.
2. Let's see:
y = 2/(x - 3)
x - 3 = 2/y
x = 2/y + 3
y^(-1) = 2/x + 3
What conclusions may we draw? (look at the values 3 and 0 in both functions).
3. Depends on the function (in my opinion).
A rational function is a mathematical function that can be written as the quotient of two polynomial functions. It is a type of algebraic function that includes variables in both the numerator and denominator.
The domain of a rational function is all the possible values that the independent variable (x) can take without making the denominator equal to zero. In other words, it is the set of all real numbers except the values that would result in division by zero.
To find the range of a rational function, you need to first determine the domain. Then, you can use algebraic techniques such as factoring, graphing, or solving for the dependent variable (y) to determine the corresponding range of values.
The common features of the graph of a rational function include a horizontal and/or vertical asymptote, a point of discontinuity, and a curve that may approach but never touch the asymptotes. The graph may also have holes or gaps at the points of discontinuity.
Rational functions can be used to model real-world situations that involve quantities that are dependent on each other. For example, they can be used to represent rates of change, such as velocity, growth, or decay. They are also commonly used in engineering, physics, and economics to solve problems involving varying quantities.