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 identifying all the x-values for which the function is defined. From the graph, observe the segment starts at x = 0 and goes to x = 2, so the domain includes values from 0 to 2. Since the graph does not show values for x \u003c 0, the domain is $$[0, 2]. $$Step 2: Determine the range of the function by looking at the y-values that the function takes on the graph. The function starts at y = 0 when x = 0 and increases linearly to y = 4 when x = 2, so the range is $$[0, 4]. $$Step 3: Find the x-intercepts by identifying points where the graph crosses the x-axis (where $$y=0). $$The graph passes through the origin (0,0), so the x-intercept is at $$x=0. $$Step 4: Find the y-intercept by identifying where the graph crosses the y-axis (where $$x=0). $$The graph passes through (0,0), so the y-intercept is $$y=0. $$Step 5: Determine the missing function values $$f(-2)$$ and $$f(2). $$Since the graph is only defined from $$x=0 to$$ $$x=2$$, $$f(-2) is $$not defined based on the graph. For $$f(2)$$, look at the point on the graph at $$x=2$$, which corresponds to $$y=4$$, so $$f(2) = 4.$$

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