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Which graph best represents a logarithmic function with the following parameters? Domain: x > 2

Which graph best represents a logarithmic function with the following parameters? Domain: x > 2

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 two graphs on Cartesian coordinate systems, each featuring a distinct curve. **Graph 1:** - The plot is on a grid with both x and y-axes ranging from -10 to 10. - The graph represents a curve starting just below y = 0, extending to the right, and increasing steeply as it approaches the y-axis and moves upward through the first quadrant. - The curve appears to be part of a regular function that increases rapidly as it moves from left to right, indicating exponential growth. **Graph 2:** - Similar coordinate setup with x and y-axes ranging from -10 to 10. - The graph shows a curve starting below y = -10 on the y-axis and moving through the fourth quadrant. The curve increases, leveling off as it moves toward y = 0. - The curve is negative at lower x-values and approaches y = 0 as x increases, indicative of a logarithmic behavior or inverse relationship. Both graphs illustrate fundamental mathematical functions, useful for exploring concepts like exponential growth and logarithmic functions.
Transcribed Image Text:The image displays two graphs on Cartesian coordinate systems, each featuring a distinct curve. **Graph 1:** - The plot is on a grid with both x and y-axes ranging from -10 to 10. - The graph represents a curve starting just below y = 0, extending to the right, and increasing steeply as it approaches the y-axis and moves upward through the first quadrant. - The curve appears to be part of a regular function that increases rapidly as it moves from left to right, indicating exponential growth. **Graph 2:** - Similar coordinate setup with x and y-axes ranging from -10 to 10. - The graph shows a curve starting below y = -10 on the y-axis and moving through the fourth quadrant. The curve increases, leveling off as it moves toward y = 0. - The curve is negative at lower x-values and approaches y = 0 as x increases, indicative of a logarithmic behavior or inverse relationship. Both graphs illustrate fundamental mathematical functions, useful for exploring concepts like exponential growth and logarithmic functions.
**Which graph best represents a logarithmic function with the following parameters?** **Domain:** \[ x > 2 \] **Range:** All real numbers **Vertical Asymptote:** \[ x = 2 \] **Graphs Description:** 1. **First Graph (Top):** - The graph shows a curve starting from the left side and moving downwards to the right, approaching but not crossing the vertical line at \( x = -3 \). The graph is decreasing and seems to have a vertical asymptote at \( x = -3 \). 2. **Second Graph (Bottom):** - The graph depicts a curve starting from the vertical line at \( x = 2 \) and moving upwards to the right. The curve approaches the vertical line \( x = 2 \) but does not cross it, indicating a vertical asymptote at \( x = 2 \). This graph matches the given parameters of the logarithmic function with a domain of \( x > 2 \).
Transcribed Image Text:**Which graph best represents a logarithmic function with the following parameters?** **Domain:** \[ x > 2 \] **Range:** All real numbers **Vertical Asymptote:** \[ x = 2 \] **Graphs Description:** 1. **First Graph (Top):** - The graph shows a curve starting from the left side and moving downwards to the right, approaching but not crossing the vertical line at \( x = -3 \). The graph is decreasing and seems to have a vertical asymptote at \( x = -3 \). 2. **Second Graph (Bottom):** - The graph depicts a curve starting from the vertical line at \( x = 2 \) and moving upwards to the right. The curve approaches the vertical line \( x = 2 \) but does not cross it, indicating a vertical asymptote at \( x = 2 \). This graph matches the given parameters of the logarithmic function with a domain of \( x > 2 \).
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