Question

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.

Accepted Answer

Step 1: Determine the domain of the function by looking at the x-values over which the graph is defined. Since the graph extends indefinitely to the left and right, the domain is all real numbers, which can be written as $$(-\infty, \infty). $$Step 2: Determine the range of the function by identifying the minimum and maximum y-values the graph attains. From the graph, the highest point is at y = 4 and the lowest point is at y = -4, so the range is $$[-4, 4]. $$Step 3: Identify the x-intercepts by finding the points where the graph crosses the x-axis (where y = 0). The graph crosses the x-axis at $$x = -11$$, $$x = 0$$, and $$x = 15$$, so the x-intercepts are $$(-11, 0)$$, $$(0, 0)$$, and $$(15, 0). $$Step 4: Identify the y-intercept by finding the point where the graph crosses the y-axis (where x = 0). The graph crosses the y-axis at $$(0, 0)$$, so the y-intercept is $$(0, 0). $$Step 5: For the missing function values indicated by question marks, use the graph to read the corresponding y-values at the given x-values. Locate each x-value on the x-axis, then find the point on the graph directly above or below it to determine the function value $$f(x).$$

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.

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주요 개념

Domain of a Function

Range of a Function

Intercepts of a Function