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Use the graphs to evaluate the expressions below. 61 5 4 3 2 1 f(x) 1 f(g(4)) = g(f(5)) = f(f(0)) = g(g(3)) = N 3 X 4 5 6-1 LO 4 3 ܠܟ 2 1 g(x) 1 2 3 4 5 X

Use the graphs to evaluate the expressions below. 61 5 4 3 2 1 f(x) 1 f(g(4)) = g(f(5)) = f(f(0)) = g(g(3)) = N 3 X 4 5 6-1 LO 4 3 ܠܟ 2 1 g(x) 1 2 3 4 5 X

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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**Using Graphs to Evaluate Composite Functions** In this lesson, we'll exercise evaluating composite functions using provided graphs for functions \( f(x) \) and \( g(x) \). **Graphs Overview:** 1. **Graph of \( f(x) \)**: - \( x \)-axis range: 0 to 6 - \( y \)-axis range: -1 to 6 - The graph points are as follows: - \( f(1) = 2 \) - \( f(2) = 4 \) - \( f(3) = 5 \) - \( f(4) = 4 \) - \( f(5) = 2 \) 2. **Graph of \( g(x) \)**: - \( x \)-axis range: 0 to 6 - \( y \)-axis range: -1 to 6 - The graph points are as follows: - \( g(1) = 4 \) - \( g(2) = 2 \) - \( g(3) = -1 \) - \( g(4) = 2 \) - \( g(5) = 4 \) **Evaluating Composite Functions:** 1. **\( f(g(4)) \)**: - First, find \( g(4) \): \[ g(4) = 2 \] - Next, find \( f(2) \): \[ f(2) = 4 \] - Therefore, \( f(g(4)) = f(2) = 4 \). 2. **\( g(f(5)) \)**: - First, find \( f(5) \): \[ f(5) = 2 \] - Next, find \( g(2) \): \[ g(2) = 2 \] - Therefore, \( g(f(5)) = g(2) = 2 \). 3. **\( f(f(0)) \)**: - First, find \( f(0) \): \( f(0) \) is not explicitly provided in the given graph, implying that additional context or explanation is needed. From the given range, we presume \( f(0) \) is outside the examined range
Transcribed Image Text:**Using Graphs to Evaluate Composite Functions** In this lesson, we'll exercise evaluating composite functions using provided graphs for functions \( f(x) \) and \( g(x) \). **Graphs Overview:** 1. **Graph of \( f(x) \)**: - \( x \)-axis range: 0 to 6 - \( y \)-axis range: -1 to 6 - The graph points are as follows: - \( f(1) = 2 \) - \( f(2) = 4 \) - \( f(3) = 5 \) - \( f(4) = 4 \) - \( f(5) = 2 \) 2. **Graph of \( g(x) \)**: - \( x \)-axis range: 0 to 6 - \( y \)-axis range: -1 to 6 - The graph points are as follows: - \( g(1) = 4 \) - \( g(2) = 2 \) - \( g(3) = -1 \) - \( g(4) = 2 \) - \( g(5) = 4 \) **Evaluating Composite Functions:** 1. **\( f(g(4)) \)**: - First, find \( g(4) \): \[ g(4) = 2 \] - Next, find \( f(2) \): \[ f(2) = 4 \] - Therefore, \( f(g(4)) = f(2) = 4 \). 2. **\( g(f(5)) \)**: - First, find \( f(5) \): \[ f(5) = 2 \] - Next, find \( g(2) \): \[ g(2) = 2 \] - Therefore, \( g(f(5)) = g(2) = 2 \). 3. **\( f(f(0)) \)**: - First, find \( f(0) \): \( f(0) \) is not explicitly provided in the given graph, implying that additional context or explanation is needed. From the given range, we presume \( f(0) \) is outside the examined range
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