The graph of a function is shown. Find value f(1) = 3, f(5) = 0, 7. What are the domain and range of f?
Understand the Problem
The question is asking to analyze a given piecewise function based on its graph. It seeks to find specific function values at certain points and identify the domain and range of the function.
Answer
The values are \(f(1) = 3\), \(f(5) = 0\), \(f(7) = -2\); domain \(D = [0, 7]\); range \(R = [-2, 3]\).
Answer for screen readers
The function values are (f(1) = 3), (f(5) = 0), and (f(7) = -2).
The domain is (D = [0, 7]) and the range is (R = [-2, 3]).
Steps to Solve
- Identify Values from the Graph From the graph, we see the following values:
- (f(1) = 3)
- (f(5) = 0)
- Also mentioned is (f(7)), which we need to check the graph for.
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Determine (f(7)) By examining the graph at (x = 7), we find that (f(7) = -2).
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Identify the Domain The domain of the function consists of the values of (x) for which (f(x)) is defined. From the graph, (x) ranges from 0 to 7. Thus, the domain is: $$ D = [0, 7] $$
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Identify the Range The range of the function consists of the possible values of (f(x)). From the graph, the highest (y) value is 3 (at (x = 1)) and the lowest is -2 (at (x = 7)). Thus, the range is: $$ R = [-2, 3] $$
The function values are (f(1) = 3), (f(5) = 0), and (f(7) = -2).
The domain is (D = [0, 7]) and the range is (R = [-2, 3]).
More Information
The values of the function at specific points can help understand the shape and behavior of the graph. The identified domain and range reflect the extremes of the function's output as (x) changes within the defined limits.
Tips
- Confusing the values of (y) from the graph or not checking the specific points properly. Always ensure to reference the graph carefully when identifying function values.
- Incorrectly determining the range by ignoring negative values or not considering all the heights of the graph. Always check the minimum and maximum points on the graph.
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