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10) Drag and drop the correct answers. The graph of the function y y=0.125 Domain: 1 9 Range: -3-2 5- 4- 3+ 2- 14 -1- -2+ -3+ -4- -5- y 0.125 2 ()* 9 -3 What is the domain and range of the function? is shown. -10 X Choices *** 00 x < 0 -∞0

10) Drag and drop the correct answers. The graph of the function y y=0.125 Domain: 1 9 Range: -3-2 5- 4- 3+ 2- 14 -1- -2+ -3+ -4- -5- y 0.125 2 ()* 9 -3 What is the domain and range of the function? is shown. -10 X Choices *** 00 x < 0 -∞0

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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### Understanding Exponential Functions #### Drag and Drop Activity: Identifying Domain and Range **Problem Statement:** The graph of the function \( y = 0.125 \left(\frac{1}{9}\right)^x \) is shown below. #### Graph Description: The graph depicts the exponential function \( y = 0.125 \left(\frac{1}{9}\right)^x \) on a coordinate plane with \( x \) and \( y \) axes ranging from -5 to 5. The curve starts at positive values when \( x \) is negative and approaches \( y = 0 \) as \( x \) increases. The function never crosses or touches the x-axis, indicating that \( y \) approaches zero but is never exactly zero. #### Choices for Domain and Range: - \( 0 < y < \infty \) - \( y < 0 \) - \( x > 0 \) - \( x < 0 \) - \( -\infty < y < \infty \) - all real numbers **Question:** What is the domain and range of the function? **Answer:** - **Domain:** All real numbers, \( -\infty < x < \infty \) - **Range:** \( 0 < y < \infty \) To complete the exercise, drag and drop the appropriate answer choices to the corresponding lines under Domain and Range. ##### Explanation: - The **domain** of the function consists of all possible values of \( x \). Since the function \( y = 0.125 \left(\frac{1}{9}\right)^x \) is defined for all real numbers, the domain is \( -\infty < x < \infty \). - The **range** of the function consists of all possible values of \( y \). Observing the graph, \( y \) takes any positive value and approaches zero as \( x \) approaches infinity but never becomes zero or negative. Hence, the range is \( 0 < y < \infty \). By understanding these concepts, you'll be able to identify the domain and range of similar exponential functions.
Transcribed Image Text:### Understanding Exponential Functions #### Drag and Drop Activity: Identifying Domain and Range **Problem Statement:** The graph of the function \( y = 0.125 \left(\frac{1}{9}\right)^x \) is shown below. #### Graph Description: The graph depicts the exponential function \( y = 0.125 \left(\frac{1}{9}\right)^x \) on a coordinate plane with \( x \) and \( y \) axes ranging from -5 to 5. The curve starts at positive values when \( x \) is negative and approaches \( y = 0 \) as \( x \) increases. The function never crosses or touches the x-axis, indicating that \( y \) approaches zero but is never exactly zero. #### Choices for Domain and Range: - \( 0 < y < \infty \) - \( y < 0 \) - \( x > 0 \) - \( x < 0 \) - \( -\infty < y < \infty \) - all real numbers **Question:** What is the domain and range of the function? **Answer:** - **Domain:** All real numbers, \( -\infty < x < \infty \) - **Range:** \( 0 < y < \infty \) To complete the exercise, drag and drop the appropriate answer choices to the corresponding lines under Domain and Range. ##### Explanation: - The **domain** of the function consists of all possible values of \( x \). Since the function \( y = 0.125 \left(\frac{1}{9}\right)^x \) is defined for all real numbers, the domain is \( -\infty < x < \infty \). - The **range** of the function consists of all possible values of \( y \). Observing the graph, \( y \) takes any positive value and approaches zero as \( x \) approaches infinity but never becomes zero or negative. Hence, the range is \( 0 < y < \infty \). By understanding these concepts, you'll be able to identify the domain and range of similar exponential functions.
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