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From the graphs of f and g in the figure, we find the following. (Assume that each point lies on the gridlines.) (f + g)(0) (0)(6 - ) (fg)(0) ()の) %3D I|||

From the graphs of f and g in the figure, we find the following. (Assume that each point lies on the gridlines.) (f + g)(0) (0)(6 - ) (fg)(0) ()の) %3D I|||

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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### Identifying Function Values from Graphs (Educational Resource) #### Problem Statement: From the graphs of \( f \) and \( g \) in the figure below, determine the following expressions at \( x = 0 \). (Assume that each point lies on the gridlines.) 1. \((f + g)(0) =\) [______] 2. \((f - g)(0) =\) [______] 3. \((fg)(0) =\) [______] 4. \(\left(\frac{f}{g}\right)(0) =\) [______] #### Graph Description: - The graph includes two functions, \( f \) and \( g \), plotted on the same set of axes with gridlines. - The function \( f \) is represented by a red curve. - The function \( g \) is represented by a blue curve. **Axes Labeled:** - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). **Gridlines and Values:** - The graph features standard Cartesian coordinates where the gridlines intersect at integer values. - The point where \( x = 0 \) is of primary interest for each function. #### Observations at \( x = 0 \): - Value of \( f(0) = 1 \) - Value of \( g(0) = 2 \) #### Calculations: 1. \((f + g)(0) = f(0) + g(0) = 1 + 2 = 3\) 2. \((f - g)(0) = f(0) - g(0) = 1 - 2 = -1\) 3. \((fg)(0) = f(0) \times g(0) = 1 \times 2 = 2\) 4. \(\left(\frac{f}{g}\right)(0) = \frac{f(0)}{g(0)} = \frac{1}{2} = 0.5\) ### Final Results: - \((f + g)(0) = 3\) - \((f - g)(0) = -1\) - \((fg)(0) = 2\) - \(\left(\frac{f}{g}\right)(0) = 0.5\)
Transcribed Image Text:### Identifying Function Values from Graphs (Educational Resource) #### Problem Statement: From the graphs of \( f \) and \( g \) in the figure below, determine the following expressions at \( x = 0 \). (Assume that each point lies on the gridlines.) 1. \((f + g)(0) =\) [______] 2. \((f - g)(0) =\) [______] 3. \((fg)(0) =\) [______] 4. \(\left(\frac{f}{g}\right)(0) =\) [______] #### Graph Description: - The graph includes two functions, \( f \) and \( g \), plotted on the same set of axes with gridlines. - The function \( f \) is represented by a red curve. - The function \( g \) is represented by a blue curve. **Axes Labeled:** - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). **Gridlines and Values:** - The graph features standard Cartesian coordinates where the gridlines intersect at integer values. - The point where \( x = 0 \) is of primary interest for each function. #### Observations at \( x = 0 \): - Value of \( f(0) = 1 \) - Value of \( g(0) = 2 \) #### Calculations: 1. \((f + g)(0) = f(0) + g(0) = 1 + 2 = 3\) 2. \((f - g)(0) = f(0) - g(0) = 1 - 2 = -1\) 3. \((fg)(0) = f(0) \times g(0) = 1 \times 2 = 2\) 4. \(\left(\frac{f}{g}\right)(0) = \frac{f(0)}{g(0)} = \frac{1}{2} = 0.5\) ### Final Results: - \((f + g)(0) = 3\) - \((f - g)(0) = -1\) - \((fg)(0) = 2\) - \(\left(\frac{f}{g}\right)(0) = 0.5\)
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