Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### Logarithmic Function Analysis

#### Task:
Analyze the graph below to identify the key features of the logarithmic function.

![Logarithmic Function Graph](image_link)

#### Graph Description:
- The graph shows a typical logarithmic curve.
- The x-axis and y-axis intersect at the origin (0,0).
- The curve passes through the point (1, 0) on the x-axis.
- The curve approaches a vertical asymptote at \( x = -2 \).

#### Options:
Select the correct statement that describes the key features of the logarithmic function:

- \( \circ \) The x-intercept is \( y = 2 \), and the graph approaches a vertical asymptote at \( y = 3 \).
- \( \circ \) The x-intercept is \( x = 2 \), and the graph approaches a vertical asymptote at \( x = 3 \).
- \( \circ \) The x-intercept is \( y = -2 \), and the graph approaches a vertical asymptote at \( y = -3 \).
- \( \circ \) The x-intercept is \( x = -2 \), and the graph approaches a vertical asymptote at \( x = -3 \).

#### Answer Explanation:
Based on the graph, the correct statement is the one that accurately describes both the x-intercept and the behavior of the graph as it approaches the vertical asymptote. The graph approaches a vertical asymptote at \( x = -2 \), making the relevant option the correct one.
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Transcribed Image Text:### Logarithmic Function Analysis #### Task: Analyze the graph below to identify the key features of the logarithmic function. ![Logarithmic Function Graph](image_link) #### Graph Description: - The graph shows a typical logarithmic curve. - The x-axis and y-axis intersect at the origin (0,0). - The curve passes through the point (1, 0) on the x-axis. - The curve approaches a vertical asymptote at \( x = -2 \). #### Options: Select the correct statement that describes the key features of the logarithmic function: - \( \circ \) The x-intercept is \( y = 2 \), and the graph approaches a vertical asymptote at \( y = 3 \). - \( \circ \) The x-intercept is \( x = 2 \), and the graph approaches a vertical asymptote at \( x = 3 \). - \( \circ \) The x-intercept is \( y = -2 \), and the graph approaches a vertical asymptote at \( y = -3 \). - \( \circ \) The x-intercept is \( x = -2 \), and the graph approaches a vertical asymptote at \( x = -3 \). #### Answer Explanation: Based on the graph, the correct statement is the one that accurately describes both the x-intercept and the behavior of the graph as it approaches the vertical asymptote. The graph approaches a vertical asymptote at \( x = -2 \), making the relevant option the correct one.
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