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5 -4 -3 2 a 2 7 -2 -34 -4 +-5+ 1 2 3 4 5 ď

5 -4 -3 2 a 2 7 -2 -34 -4 +-5+ 1 2 3 4 5 ď

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Finding the Domain and Range of a Function from its Graph Below is the graph of a function. The graph is displayed on a coordinate plane, with both the x-axis and y-axis marked. The function starts at the point \((-4, -5)\), represented by a solid dot, indicating that this point is included in the function. The function then curves upward and reaches a maximum at the point \((0, 4)\), then curves downward and ends at the point \((1.5, 3)\), represented by an open dot, indicating that this point is not included in the function. #### Graph Details - The x-axis ranges from -5 to 5. - The y-axis ranges from -5 to 5. - The function appears to be a piece of a parabola that starts at \((-4, -5)\) and extends to \((1.5, 3)\). #### Domain and Range **Domain**: The domain of a function is the set of all possible input values (x-values). According to the graph: - The function includes all x-values from -4 to 1.5. The domain can be written in interval notation as: \[ \text{Domain}: [-4, 1.5) \] **Range**: The range of a function is the set of all possible output values (y-values). According to the graph: - The function reaches its minimum y-value at -5 and its maximum y-value at 4. However, since the function does not include the point at \((1.5, 3)\), the maximum y-value for the range should be considered as slightly below 4. The range can be written in interval notation as: \[ \text{Range}: [-5, 4] \] Please fill in your answers based on this explanation. **Domain:** \[ [-4, 1.5) \] **Range:** \[ [-5, 4] \]
Transcribed Image Text:### Finding the Domain and Range of a Function from its Graph Below is the graph of a function. The graph is displayed on a coordinate plane, with both the x-axis and y-axis marked. The function starts at the point \((-4, -5)\), represented by a solid dot, indicating that this point is included in the function. The function then curves upward and reaches a maximum at the point \((0, 4)\), then curves downward and ends at the point \((1.5, 3)\), represented by an open dot, indicating that this point is not included in the function. #### Graph Details - The x-axis ranges from -5 to 5. - The y-axis ranges from -5 to 5. - The function appears to be a piece of a parabola that starts at \((-4, -5)\) and extends to \((1.5, 3)\). #### Domain and Range **Domain**: The domain of a function is the set of all possible input values (x-values). According to the graph: - The function includes all x-values from -4 to 1.5. The domain can be written in interval notation as: \[ \text{Domain}: [-4, 1.5) \] **Range**: The range of a function is the set of all possible output values (y-values). According to the graph: - The function reaches its minimum y-value at -5 and its maximum y-value at 4. However, since the function does not include the point at \((1.5, 3)\), the maximum y-value for the range should be considered as slightly below 4. The range can be written in interval notation as: \[ \text{Range}: [-5, 4] \] Please fill in your answers based on this explanation. **Domain:** \[ [-4, 1.5) \] **Range:** \[ [-5, 4] \]
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