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g(x) = 16 14 12 10 2 6 3, if 0 ≤X<2 Dif if 2 ≤x< 11, if DIE ≤x<0 if 6 < x < 8

g(x) = 16 14 12 10 2 6 3, if 0 ≤X<2 Dif if 2 ≤x< 11, if DIE ≤x<0 if 6 < x < 8

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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**Hotspot Label** The piecewise function \( y = g(x) \) is given in the graph below. Fill in the blanks to complete the function that is represented by the graph. - Press each hotspot. - Label the corresponding number below with the requested value.
Transcribed Image Text:**Hotspot Label** The piecewise function \( y = g(x) \) is given in the graph below. Fill in the blanks to complete the function that is represented by the graph. - Press each hotspot. - Label the corresponding number below with the requested value.
The image presents a step function graph and its corresponding piecewise function notation. Here's the transcribed and detailed explanation: ### Graph Description The graph is a step function plotted on a coordinate plane. The x-axis is labeled from 0 to 8, and the y-axis from 0 to 16. The function has four distinct segments: 1. From \( x = 0 \) to \( x = 2 \), the function value is constant at 3. The line segment starts with a closed circle at \( (0, 3) \) and ends with an open circle at \( (2, 3) \). 2. From \( x = 2 \) to \( x = 4 \), the function value is 7. A closed circle is at \( (2, 7) \) and an open circle at \( (4, 7) \). 3. From \( x = 4 \) to \( x = 6 \), the function value is 11, starting with a closed circle at \( (4, 11) \) and ending with an open circle at \( (6, 11) \). 4. From \( x = 6 \) to \( x = 8 \), the function value is 15, indicated by a closed circle at \( (6, 15) \) and an open circle at \( (8, 15) \). ### Piecewise Function Notation The step function \( g(x) \) is defined as follows: \[ g(x) = \begin{cases} 3, & \text{if } 0 \leq x < 2 \\ 7, & \text{if } 2 \leq x < 4 \\ 11, & \text{if } 4 \leq x < 6 \\ 15, & \text{if } 6 \leq x < 8 \\ \end{cases} \] This function notation describes how the value of \( g(x) \) changes over different intervals on the x-axis. Each interval has a constant y-value, creating a series of horizontal steps.
Transcribed Image Text:The image presents a step function graph and its corresponding piecewise function notation. Here's the transcribed and detailed explanation: ### Graph Description The graph is a step function plotted on a coordinate plane. The x-axis is labeled from 0 to 8, and the y-axis from 0 to 16. The function has four distinct segments: 1. From \( x = 0 \) to \( x = 2 \), the function value is constant at 3. The line segment starts with a closed circle at \( (0, 3) \) and ends with an open circle at \( (2, 3) \). 2. From \( x = 2 \) to \( x = 4 \), the function value is 7. A closed circle is at \( (2, 7) \) and an open circle at \( (4, 7) \). 3. From \( x = 4 \) to \( x = 6 \), the function value is 11, starting with a closed circle at \( (4, 11) \) and ending with an open circle at \( (6, 11) \). 4. From \( x = 6 \) to \( x = 8 \), the function value is 15, indicated by a closed circle at \( (6, 15) \) and an open circle at \( (8, 15) \). ### Piecewise Function Notation The step function \( g(x) \) is defined as follows: \[ g(x) = \begin{cases} 3, & \text{if } 0 \leq x < 2 \\ 7, & \text{if } 2 \leq x < 4 \\ 11, & \text{if } 4 \leq x < 6 \\ 15, & \text{if } 6 \leq x < 8 \\ \end{cases} \] This function notation describes how the value of \( g(x) \) changes over different intervals on the x-axis. Each interval has a constant y-value, creating a series of horizontal steps.
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