Use the graphs of f and g to solve Exercises 83–90.
Find the domain of ƒ/g.

Key Concepts

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For rational functions, like ƒ/g, the domain excludes any values that make the denominator zero, as division by zero is undefined. Understanding the domain is crucial for determining where the function can be evaluated.

Rational Functions

A rational function is a function that can be expressed as the ratio of two polynomials. In the case of ƒ/g, it is important to analyze both the numerator (f) and the denominator (g) to identify any restrictions on the domain. The behavior of these functions can vary significantly based on their graphs, particularly at points where the denominator approaches zero.

Graph Interpretation

Interpreting graphs of functions is essential for understanding their behavior visually. The graphs of f and g provide insights into their values at specific points, including where g(x) equals zero, which directly affects the domain of ƒ/g. By analyzing the graphs, one can identify critical points and intervals that determine the overall domain of the rational function.