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. Step 1: Identify the domain of the function by looking at the x-values for which the function has points plotted. From the graph, the points are plotted at x = -5, -4, -3, -2, -1, 1, 2, 3, and 4. So, the domain is the set of these x-values.
2. Step 2: Determine the range of the function by noting the y-values of the plotted points. From the graph, all points lie on the line y = -2, so the range is just the single value y = -2.
3. Step 3: Find the x-intercepts by checking where the graph crosses the x-axis (where y = 0). Since all points have y = -2, the graph does not cross the x-axis, so there are no x-intercepts.
4. Step 4: Find the y-intercept by checking the value of the function at x = 0. Since there is no point plotted at x = 0, the function has no y-intercept.
5. Step 5: To find the value of f(-5) + f(4), read the y-values of the points at x = -5 and x = 4 from the graph. Both points have y = -2, so add these two values together to get the sum.

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 helps determine which x-values can be used to find corresponding y-values.

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 is the vertical spread of the points or curve. Understanding the range helps in knowing the limits of the function's output values.

Function Values and Intercepts

Function values are the y-values corresponding to specific x-values, denoted as f(x). The x-intercepts are points where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0). These points are crucial for analyzing the behavior and key features of the function.