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

Verified step by step guidance

1. Identify the domain of the function $f(x)$ by observing the x-values over which the graph of $f(x)$ is defined.
2. Identify the domain of the function $g(x)$ by observing the x-values over which the graph of $g(x)$ is defined.
3. Determine the intersection of the domains of $f(x)$ and $g(x)$, as the domain of $f+g$ is the set of x-values common to both functions.
4. Note any discontinuities or breaks in the graphs of $f(x)$ and $g(x)$ that might affect the domain of $f+g$.
5. Express the domain of $f+g$ as an interval or a union of intervals, based on the common x-values identified.

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 functions f and g, the domain is determined by the x-values for which both functions yield valid outputs. Understanding the domain is crucial for operations like addition, as the resulting function ƒ + g can only be evaluated where both f and g are defined.

Addition of Functions

The addition of two functions, denoted as (f + g)(x), involves combining their outputs for each input x. This means that for any x in the domain of both functions, (f + g)(x) = f(x) + g(x). To find the domain of the sum, one must identify the intersection of the domains of f and g, ensuring that both functions are defined at those x-values.

Graph Interpretation

Interpreting the graphs of functions f and g is essential for understanding their behavior and determining their domains. The graph visually represents the values of the functions, allowing one to see where they are defined (i.e., where the graph exists) and where they are not. By analyzing the points on the graph, one can easily identify the x-values that belong to the domain of ƒ + g.