A function fis given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. f(x) = x2; shift 2 units to the left and reflect in the x-axis y =
A function fis given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. f(x) = x2; shift 2 units to the left and reflect in the x-axis y =
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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![**Problem Statement:**
A function \( f \) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.
Given function:
\[ f(x) = x^2 \]
Transformations:
1. Shift 2 units to the left.
2. Reflect in the x-axis.
**Solution:**
1. **Shift 2 Units to the Left:**
To shift the graph 2 units to the left, replace \( x \) with \( x + 2 \).
\[
f(x) = (x + 2)^2
\]
2. **Reflect in the x-axis:**
To reflect the graph in the x-axis, multiply the entire function by \(-1\).
\[
f(x) = -(x + 2)^2
\]
**Final Transformed Equation:**
\[ y = -(x + 2)^2 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff63b92e4-879d-4142-a3ba-8741f16c356f%2F1c033f9c-32cf-4c26-8bfd-995249d1aade%2Fpkpopsjm_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A function \( f \) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.
Given function:
\[ f(x) = x^2 \]
Transformations:
1. Shift 2 units to the left.
2. Reflect in the x-axis.
**Solution:**
1. **Shift 2 Units to the Left:**
To shift the graph 2 units to the left, replace \( x \) with \( x + 2 \).
\[
f(x) = (x + 2)^2
\]
2. **Reflect in the x-axis:**
To reflect the graph in the x-axis, multiply the entire function by \(-1\).
\[
f(x) = -(x + 2)^2
\]
**Final Transformed Equation:**
\[ y = -(x + 2)^2 \]
![**Function Transformations**
A function \( f \) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.
Given:
\[ f(x) = |x| \]
Transformations:
- Shift 3 units to the left.
- Shift downward 8 units.
Determine the final equation:
\[ y = \]
In the box below, enter the equation for the transformed function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff63b92e4-879d-4142-a3ba-8741f16c356f%2F1c033f9c-32cf-4c26-8bfd-995249d1aade%2Fg5xb8gs_processed.png&w=3840&q=75)
Transcribed Image Text:**Function Transformations**
A function \( f \) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.
Given:
\[ f(x) = |x| \]
Transformations:
- Shift 3 units to the left.
- Shift downward 8 units.
Determine the final equation:
\[ y = \]
In the box below, enter the equation for the transformed function.
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