In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

Verified step by step guidance

1. Identify the domain by listing all the x-coordinates of the points on the graph. The domain consists of the x-values where the function is defined.
2. Determine the range by listing all the y-coordinates of the points on the graph. The range consists of the y-values that the function takes.
3. Find the x-intercepts by checking where the graph crosses the x-axis. These are points where the y-coordinate is zero.
4. Find the y-intercept by checking where the graph crosses the y-axis. This is the point where the x-coordinate is zero.
5. For the missing function values indicated by question marks, use the given points to match the x-values with their corresponding y-values from the graph.

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. In a graph, the domain corresponds to the horizontal extent of the plotted points or curve. Identifying the domain involves listing all x-coordinates of the points shown.

Range of a Function

The range of a function is the set of all possible output values (y-values) that the function can produce. On a graph, the range corresponds to the vertical spread of the points or curve. To find the range, list all y-coordinates of the points on the graph.

Intercepts of a Function

Intercepts are points where the graph crosses the axes. The x-intercepts occur where the function's output is zero (y=0), and the y-intercept occurs where the input is zero (x=0). Identifying intercepts helps understand the function's behavior and is done by checking points on the axes.