Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Solve correctly write the domain and range of h using interval notation
The text provided is: "The entire graph of the function \(h\) is shown in the figure below. Write the domain and range of \(h\) using interval notation." ### Graph Description: The graph is displayed on a coordinate plane with the x-axis and y-axis marked. Here are the details: - **Domain**: The x-values span from negative infinity to positive infinity. However, the function appears to be discontinuous at certain points, specifically: - There is an open circle at \(x = -3\). - There is another open circle at \(x = 4\). - **Range**: The y-values extend from negative infinity upwards: - The lowest point of the curve appears to reach potentially \(-\infty\). - The function is discontinuous at the following y-values: - There is an open circle at \(y = -4\). - There is another open circle at \(y = 4\). The graph includes a curve with two distinct portions: - The left portion starts from negative infinity, increases and reaches as high as \(y=4\) where an open circle is present before decreasing. - The right portion starts at \(x=4\) increases up to a peak just below \(y=5\) and continues further right as it descends toward infinity. ### Interpretation for Domain and Range (using interval notation): - **Domain**: The domain of function \(h\) can be described as \( (-\infty, -3) \cup (-3, 4) \cup (4, \infty) \). - **Range**: The range of function \(h\) is \( (-\infty, 4) \). The function does not reach the value \(y = 4\) at \(x = 4\).
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Transcribed Image Text:The text provided is: "The entire graph of the function \(h\) is shown in the figure below. Write the domain and range of \(h\) using interval notation." ### Graph Description: The graph is displayed on a coordinate plane with the x-axis and y-axis marked. Here are the details: - **Domain**: The x-values span from negative infinity to positive infinity. However, the function appears to be discontinuous at certain points, specifically: - There is an open circle at \(x = -3\). - There is another open circle at \(x = 4\). - **Range**: The y-values extend from negative infinity upwards: - The lowest point of the curve appears to reach potentially \(-\infty\). - The function is discontinuous at the following y-values: - There is an open circle at \(y = -4\). - There is another open circle at \(y = 4\). The graph includes a curve with two distinct portions: - The left portion starts from negative infinity, increases and reaches as high as \(y=4\) where an open circle is present before decreasing. - The right portion starts at \(x=4\) increases up to a peak just below \(y=5\) and continues further right as it descends toward infinity. ### Interpretation for Domain and Range (using interval notation): - **Domain**: The domain of function \(h\) can be described as \( (-\infty, -3) \cup (-3, 4) \cup (4, \infty) \). - **Range**: The range of function \(h\) is \( (-\infty, 4) \). The function does not reach the value \(y = 4\) at \(x = 4\).
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