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Is the graph that of a function? No Yes What are the domain and range of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The domain is The range is (Type your answers in interval notation.) OB. The graph is not that of a function. What are the intercepts of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) O B. The graph is not that of a function. If the graph is that of a function, determine what kinds of symmetry it has. Select all that apply. A. The graph is symmetrical with respect to the y-axis. B. The graph is symmetrical with respect to the x-axis. C. The graph is symmetrical with respect to the origin. D. The graph is not symmetrical. E. The graph is not that of a function.

Is the graph that of a function? No Yes What are the domain and range of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The domain is The range is (Type your answers in interval notation.) OB. The graph is not that of a function. What are the intercepts of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) O B. The graph is not that of a function. If the graph is that of a function, determine what kinds of symmetry it has. Select all that apply. A. The graph is symmetrical with respect to the y-axis. B. The graph is symmetrical with respect to the x-axis. C. The graph is symmetrical with respect to the origin. D. The graph is not symmetrical. E. The graph is not that of a function.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The image displays a graph of a hyperbola on a Cartesian coordinate system. The x-axis and y-axis intersect at the origin (0,0). The grid is marked in increments of 6 along both axes, ranging from -12 to 12. ### Description of the Graph: - **Axes:** - The horizontal axis is labeled as the x-axis. - The vertical axis is labeled as the y-axis. - **Plot:** - The hyperbola opens horizontally, with two branches extending towards the positive and negative x-directions. - Each branch approaches but never touches two asymptotes, aligning with a typical hyperbolic structure. - **Asymptotes:** - The asymptotes of the hyperbola seem to be indicated by the direction of the branches. ### Characteristics of the Hyperbola: - **Central Symmetry:** - The graph is symmetrical around the origin. - Each branch is a mirror image of the other along the y-axis. - **Vertex and Center:** - The center of the hyperbola is at the origin (0,0), where the x and y axes intersect. - The vertices of the hyperbola are located on the x-axis at points near (-6, 0) and (6, 0). - **Orientation:** - The hyperbola is oriented horizontally. This graph serves as a visual representation of a mathematical concept, illustrating the shape and properties of a hyperbolic function on a two-dimensional plane.
Transcribed Image Text:The image displays a graph of a hyperbola on a Cartesian coordinate system. The x-axis and y-axis intersect at the origin (0,0). The grid is marked in increments of 6 along both axes, ranging from -12 to 12. ### Description of the Graph: - **Axes:** - The horizontal axis is labeled as the x-axis. - The vertical axis is labeled as the y-axis. - **Plot:** - The hyperbola opens horizontally, with two branches extending towards the positive and negative x-directions. - Each branch approaches but never touches two asymptotes, aligning with a typical hyperbolic structure. - **Asymptotes:** - The asymptotes of the hyperbola seem to be indicated by the direction of the branches. ### Characteristics of the Hyperbola: - **Central Symmetry:** - The graph is symmetrical around the origin. - Each branch is a mirror image of the other along the y-axis. - **Vertex and Center:** - The center of the hyperbola is at the origin (0,0), where the x and y axes intersect. - The vertices of the hyperbola are located on the x-axis at points near (-6, 0) and (6, 0). - **Orientation:** - The hyperbola is oriented horizontally. This graph serves as a visual representation of a mathematical concept, illustrating the shape and properties of a hyperbolic function on a two-dimensional plane.
**Is the graph that of a function?** - ☐ No - ☐ Yes **What are the domain and range of the function?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - ☐ A. The domain is [___]. The range is [___]. (Type your answers in interval notation.) - ☐ B. The graph is not that of a function. **What are the intercepts of the function?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - ☐ A. The intercept(s) is/are [___]. (Type an ordered pair. Use a comma to separate answers as needed.) - ☐ B. The graph is not that of a function. **If the graph is that of a function, determine what kinds of symmetry it has.** Select all that apply. - ☐ A. The graph is symmetrical with respect to the y-axis. - ☐ B. The graph is symmetrical with respect to the x-axis. - ☐ C. The graph is symmetrical with respect to the origin. - ☐ D. The graph is not symmetrical. - ☐ E. The graph is not that of a function.
Transcribed Image Text:**Is the graph that of a function?** - ☐ No - ☐ Yes **What are the domain and range of the function?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - ☐ A. The domain is [___]. The range is [___]. (Type your answers in interval notation.) - ☐ B. The graph is not that of a function. **What are the intercepts of the function?** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - ☐ A. The intercept(s) is/are [___]. (Type an ordered pair. Use a comma to separate answers as needed.) - ☐ B. The graph is not that of a function. **If the graph is that of a function, determine what kinds of symmetry it has.** Select all that apply. - ☐ A. The graph is symmetrical with respect to the y-axis. - ☐ B. The graph is symmetrical with respect to the x-axis. - ☐ C. The graph is symmetrical with respect to the origin. - ☐ D. The graph is not symmetrical. - ☐ E. The graph is not that of a function.
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