The graph of f(in blue) is translated a whole number of units horizontally and vertically to obtain the graph of g (in red). The function f is defined by ƒ(x) = |x|. Write down the expression for g(x). -6 -5 4 g(x) = 0 Continue Ty 8- 7 6- 5- -2- -4- g 6. 0|0| X ?
The graph of f(in blue) is translated a whole number of units horizontally and vertically to obtain the graph of g (in red). The function f is defined by ƒ(x) = |x|. Write down the expression for g(x). -6 -5 4 g(x) = 0 Continue Ty 8- 7 6- 5- -2- -4- g 6. 0|0| X ?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Translation of Graphs
The graph of function \( f \) (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of function \( g \) (in red).
The function \( f \) is defined by \( f(x) = |x| \). Write down the expression for \( g(x) \).
#### Explanation of Graphs
The chart shows two graphs on a coordinate plane:
1. **The blue graph** represents the original function \( f(x) = |x| \). The blue \( V \)-shaped graph has its vertex at the origin \((0, 0)\).
2. **The red graph** represents the translated function \( g(x) \). The red \( V \)-shaped graph has its vertex at the point \((2, -3)\).
#### Finding the Translated Function
Given that the vertex of the function \( f \) at \( (0, 0) \) has been translated to the vertex of \( g \) at \( (2, -3) \), the graph has been shifted 2 units to the right and 3 units down.
Hence, the expression for \( g(x) \) can be written as:
\[ g(x) = |x - 2| - 3 \]
#### Input Area
Below the graph, there is an input area where students are expected to write their answer:
\[ g(x) = \_\_\_\_\_ \]
#### Action Buttons
Three action buttons appear next to the input area:
- A blank space (for the student to input the translation expression).
- An "X" button, likely for clearing the input.
- A circular arrow (for resetting the problem).
- A question mark for hints or help.
#### Conclusion
The problem statement, graphs, and expected operations to determine the expression for \( g(x) \) from \( f(x) \) are outlined for educational purposes.
##### Learn More on Translating Graphs
- [Graph Translations](#)
- [Function Transformations](#)
Continue button at the bottom is for proceeding to the next step or submitting the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e5ca973-b1e1-443b-b3b9-d9d4a915d4d1%2Fdc3389db-41e2-44e3-ac74-646a486c675c%2Fef3shcg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Translation of Graphs
The graph of function \( f \) (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of function \( g \) (in red).
The function \( f \) is defined by \( f(x) = |x| \). Write down the expression for \( g(x) \).
#### Explanation of Graphs
The chart shows two graphs on a coordinate plane:
1. **The blue graph** represents the original function \( f(x) = |x| \). The blue \( V \)-shaped graph has its vertex at the origin \((0, 0)\).
2. **The red graph** represents the translated function \( g(x) \). The red \( V \)-shaped graph has its vertex at the point \((2, -3)\).
#### Finding the Translated Function
Given that the vertex of the function \( f \) at \( (0, 0) \) has been translated to the vertex of \( g \) at \( (2, -3) \), the graph has been shifted 2 units to the right and 3 units down.
Hence, the expression for \( g(x) \) can be written as:
\[ g(x) = |x - 2| - 3 \]
#### Input Area
Below the graph, there is an input area where students are expected to write their answer:
\[ g(x) = \_\_\_\_\_ \]
#### Action Buttons
Three action buttons appear next to the input area:
- A blank space (for the student to input the translation expression).
- An "X" button, likely for clearing the input.
- A circular arrow (for resetting the problem).
- A question mark for hints or help.
#### Conclusion
The problem statement, graphs, and expected operations to determine the expression for \( g(x) \) from \( f(x) \) are outlined for educational purposes.
##### Learn More on Translating Graphs
- [Graph Translations](#)
- [Function Transformations](#)
Continue button at the bottom is for proceeding to the next step or submitting the answer.
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