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Use the graphs of f and g to evaluate the functions. (b) 3 2 1 (f- g)(¹) (fg)(1) y = f(x) 1 2 2 1 1 y = g(x) 2

Use the graphs of f and g to evaluate the functions. (b) 3 2 1 (f- g)(¹) (fg)(1) y = f(x) 1 2 2 1 1 y = g(x) 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 58E
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### Evaluating Functions Using Graphs #### Understanding the Graphs - **Graph of \(y = f(x)\)** - This graph displays a piecewise linear function. - Coordinates of notable points: - \((0, 4)\) - \((1, 2)\) - \((2, 1)\) - \((3, 3)\) - The graph starts at point \((0, 4)\), undergoes a descending slope to \((2, 1)\), and then ascends again at point \((3, 3)\). - **Graph of \(y = g(x)\)** - This graph represents another piecewise linear function. - Coordinates of notable points: - \((0, 4)\) - \((1, 3)\) - \((2, 2)\) - \((3, 1)\) - \((4, 0)\) - The graph starts at point \((0, 4)\) and continuously decreases to \((4, 0)\). #### Tasks 1. **Evaluate \( (f - g)(1) \)** 2. **Evaluate \( (fg)(1) \)** __Solution Steps:__ - To find \((f - g)(x)\) at \(x = 1\): - Determine \(f(1)\) from the graph of \(y = f(x)\). - Determine \(g(1)\) from the graph of \(y = g(x)\). - Compute \((f - g)(1) = f(1) - g(1)\). - To find \( (fg)(x) \) at \( x = 1 \): - Determine \( f(1) \) from the graph of \( y = f(x) \). - Determine \( g(1) \) from the graph of \( y = g(x) \). - Compute \((fg)(1) = f(1) \cdot g(1)\). Below the graphs, there are fields to fill in the values of \((f - g)(1)\) and \((fg)(1)\): (a) \( (f - g)(1) \) ___________________ (b) \( (fg)(1) \) ___________________ Make sure to read the values
Transcribed Image Text:### Evaluating Functions Using Graphs #### Understanding the Graphs - **Graph of \(y = f(x)\)** - This graph displays a piecewise linear function. - Coordinates of notable points: - \((0, 4)\) - \((1, 2)\) - \((2, 1)\) - \((3, 3)\) - The graph starts at point \((0, 4)\), undergoes a descending slope to \((2, 1)\), and then ascends again at point \((3, 3)\). - **Graph of \(y = g(x)\)** - This graph represents another piecewise linear function. - Coordinates of notable points: - \((0, 4)\) - \((1, 3)\) - \((2, 2)\) - \((3, 1)\) - \((4, 0)\) - The graph starts at point \((0, 4)\) and continuously decreases to \((4, 0)\). #### Tasks 1. **Evaluate \( (f - g)(1) \)** 2. **Evaluate \( (fg)(1) \)** __Solution Steps:__ - To find \((f - g)(x)\) at \(x = 1\): - Determine \(f(1)\) from the graph of \(y = f(x)\). - Determine \(g(1)\) from the graph of \(y = g(x)\). - Compute \((f - g)(1) = f(1) - g(1)\). - To find \( (fg)(x) \) at \( x = 1 \): - Determine \( f(1) \) from the graph of \( y = f(x) \). - Determine \( g(1) \) from the graph of \( y = g(x) \). - Compute \((fg)(1) = f(1) \cdot g(1)\). Below the graphs, there are fields to fill in the values of \((f - g)(1)\) and \((fg)(1)\): (a) \( (f - g)(1) \) ___________________ (b) \( (fg)(1) \) ___________________ Make sure to read the values
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