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b) What do you notice about the graphs? Do you notice anything about the y-values in the table for y = 3*? %3D c) Does the exponential function represent exponential growth or exponential decay? Give two ways of finding this answer.

b) What do you notice about the graphs? Do you notice anything about the y-values in the table for y = 3*? %3D c) Does the exponential function represent exponential growth or exponential decay? Give two ways of finding this answer.

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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Need help answering b and c
## Part Four **Graphing Exponential and Logarithmic Functions** ### Task: Graph \( y = \log_3 x \) and \( y = 3^x \) on the same axis using a table. You may want to use two colors to separate the graphs. #### Table of Values: | \( x \) | \( y = \log_3 x \) | \( y = 3^x \) | |---------|--------------------|---------------| | -2 | - | 0.1111 | | -1 | - | 0.3333 | | 0 | - | 1 | | 1 | 0 | 3 | | 2 | 0.6309 | 9 | | 3 | 1 | 27 | ### Explanation of the Graph: The graph presents two functions plotted on the same set of axes: - **Logarithmic Function \( y = \log_3 x \)**: - This curve passes through the point (1, 0) and is defined for \( x > 0 \). It rises slowly, increasing as \( x \) increases. - The curve is not defined for negative \( x \) values or at \( x = 0 \). - **Exponential Function \( y = 3^x \)**: - This curve passes through the point (0, 1) and rises steeply as \( x \) increases, displaying exponential growth. - For negative \( x \) values, the function yields fractional results, approaching zero but never touching the x-axis. ### Questions: **b) Observations:** - Notice that as \( x \) increases, \( y = 3^x \) grows rapidly, illustrating exponential growth. - The \( y \)-values for the logarithmic function \( y = \log_3 x \) increase slower and are only positive for \( x > 1 \). **c) Exponential Growth or Decay:** - The function \( y = 3^x \) represents *exponential growth* since the base (3) is greater than 1. - Indicators of growth include the rapidly increasing \( y \)-values as \( x \) becomes larger and the steep upward curve on the graph.
Transcribed Image Text:## Part Four **Graphing Exponential and Logarithmic Functions** ### Task: Graph \( y = \log_3 x \) and \( y = 3^x \) on the same axis using a table. You may want to use two colors to separate the graphs. #### Table of Values: | \( x \) | \( y = \log_3 x \) | \( y = 3^x \) | |---------|--------------------|---------------| | -2 | - | 0.1111 | | -1 | - | 0.3333 | | 0 | - | 1 | | 1 | 0 | 3 | | 2 | 0.6309 | 9 | | 3 | 1 | 27 | ### Explanation of the Graph: The graph presents two functions plotted on the same set of axes: - **Logarithmic Function \( y = \log_3 x \)**: - This curve passes through the point (1, 0) and is defined for \( x > 0 \). It rises slowly, increasing as \( x \) increases. - The curve is not defined for negative \( x \) values or at \( x = 0 \). - **Exponential Function \( y = 3^x \)**: - This curve passes through the point (0, 1) and rises steeply as \( x \) increases, displaying exponential growth. - For negative \( x \) values, the function yields fractional results, approaching zero but never touching the x-axis. ### Questions: **b) Observations:** - Notice that as \( x \) increases, \( y = 3^x \) grows rapidly, illustrating exponential growth. - The \( y \)-values for the logarithmic function \( y = \log_3 x \) increase slower and are only positive for \( x > 1 \). **c) Exponential Growth or Decay:** - The function \( y = 3^x \) represents *exponential growth* since the base (3) is greater than 1. - Indicators of growth include the rapidly increasing \( y \)-values as \( x \) becomes larger and the steep upward curve on the graph.
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