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Use the graph of y=f(x) to graph the function g(x) = f(x) + 1. y = f(x) Q A A ✔ Choose the correct graph of g below. O A. O C. N Q G O B. A O D. Ay OU

Use the graph of y=f(x) to graph the function g(x) = f(x) + 1. y = f(x) Q A A ✔ Choose the correct graph of g below. O A. O C. N Q G O B. A O D. Ay OU

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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Question
Use the graph of
y=f(x)
to graph the function
g(x)=f(x)+1.
## Transcription for Educational Website ### Task: Use the graph of \( y = f(x) \) to graph the function \( g(x) = f(x) + 1 \). ### Graph: The initial graph displays \( y = f(x) \) as a blue line graph on a coordinate plane. The x and y axes range from \(-8\) to \(8\). The graph features distinct points with changes in direction between these points: - From \((-6, -3)\) to \((-4, 2)\). - From \((-4, 2)\) to \((-2, 0)\). - From \((-2, 0)\) to \((0, 4)\). - From \((0, 4)\) to \((2, 2)\). ### Task Objective: Choose the correct graph of \( g(x) = f(x) + 1 \) from the given options. ### Options: - **A.** Graph displaying a similar layout to \( f(x) \), but each y-coordinate is increased by 1. - **B.** Incorrect option. - **C.** Incorrect option. - **D.** Incorrect option. ### Explanation: The function \( g(x) = f(x) + 1 \) represents a vertical translation of \( f(x) \) by one unit upwards. Thus, each point on the graph \( y = f(x) \) will be shifted up by one unit, corresponding to the correct option A.
Transcribed Image Text:## Transcription for Educational Website ### Task: Use the graph of \( y = f(x) \) to graph the function \( g(x) = f(x) + 1 \). ### Graph: The initial graph displays \( y = f(x) \) as a blue line graph on a coordinate plane. The x and y axes range from \(-8\) to \(8\). The graph features distinct points with changes in direction between these points: - From \((-6, -3)\) to \((-4, 2)\). - From \((-4, 2)\) to \((-2, 0)\). - From \((-2, 0)\) to \((0, 4)\). - From \((0, 4)\) to \((2, 2)\). ### Task Objective: Choose the correct graph of \( g(x) = f(x) + 1 \) from the given options. ### Options: - **A.** Graph displaying a similar layout to \( f(x) \), but each y-coordinate is increased by 1. - **B.** Incorrect option. - **C.** Incorrect option. - **D.** Incorrect option. ### Explanation: The function \( g(x) = f(x) + 1 \) represents a vertical translation of \( f(x) \) by one unit upwards. Thus, each point on the graph \( y = f(x) \) will be shifted up by one unit, corresponding to the correct option A.
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