Consider the following functions. Sketch the region bounded by the graphs of the functions. ### Analyzing Bounded Regions by Functions#### Problem Statement:Consider the following functions:\[ f(x) = \sqrt[3]{x - 7} \]\[ g(x) = x - 7 \]#### Objective:Sketch the region bounded by the graphs of the functions.#### Graphical Analysis:The image presents four graphs, each plotting the region bounded by the given functions \( f(x) \) and \( g(x) \). Here's a detailed description of each graph:**Top-Left Graph:**- The \(x\)-axis ranges from 0 to 8.- The \(y\)-axis ranges from -2 to 2.- The graph of \( f(x) \) is a cubic root function shifted right by 7 units.- The graph of \( g(x) \) is a linear function also shifted downwards.- The bounded region is shaded in blue between the curves.**Top-Right Graph:**- The \(x\)-axis ranges from -8 to 0.- The \(y\)-axis ranges from -2 to 2.- The graph of \( f(x) \) again shows a cubic root function, but reflected.- The graph of \( g(x) \) intersects similarly as in the top-left graph.- The bounded region is shaded in blue.**Bottom-Left Graph:**- The \(x\)-axis ranges from 0 to 8.- The \(y\)-axis ranges from -2 to 2.- The graphs of \( f(x) \) and \( g(x) \) appear similar to the top-left graph but are extending differently.- The shaded area is still between the two curves.**Bottom-Right Graph:**- The \(x\)-axis ranges from -8 to 0.- The \(y\)-axis ranges from -2 to 2.- The graph of \( f(x) \) mirrors the bottom-left graph.- The graph of \( g(x) \) follows the same pattern.- The blue region represents the bounded area.#### Task:After analyzing the graphs, calculate the area of the region bounded by \( f(x) \) and \( g(x) \).**Find the area of the region.**\[ \boxed{\phantom{0}} \]

Answered: Image /qna-images/answer/38dca044-cbcd-4ccd-b5d8-11a90b364ee5.jpg

Answered: f(x) = √√√x-7 g(x) = x - 7 Sketch the…

f(x) = √√√x-7 g(x) = x - 7 Sketch the region bounded by the graphs of the functions. O- y 2 1 V 2 4 6 8 X -8 -6 -4 -2 y X

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Functions And Their Graphs

Section2.4: A Library Of Parent Functions

Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...

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Consider the following functions.

Sketch the region bounded by the graphs of the functions.

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