Write an equation for the graph of the parent function √x after it has been horizontally shifted 3 units to the right, shifted down vertically 7 units, and then stretched vertically by a factor of 6.
Write an equation for the graph of the parent function √x after it has been horizontally shifted 3 units to the right, shifted down vertically 7 units, and then stretched vertically by a factor of 6.
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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Answer the math questions show in the image below
![**Transcription for Educational Website:**
1. **Transformation and Equation Writing:**
Write an equation for the graph of the parent function \( \sqrt{x} \) after it has been horizontally shifted 3 units to the right, shifted down vertically 7 units, and then stretched vertically by a factor of 6.
2. **Average Rate of Change:**
Let \( k(x) = (x + 2)^2 - 5 \). Find the average rate of change of \( k(x) \) between \( x = -3 \) and \( x = 6 \).
3. **Graph and Table Analysis:**
The graph of \( f(x) \) is provided below, along with a table of selected values for the function \( g(x) \).
- **Graph Description:**
The graph of \( f(x) \) is a piecewise linear function with notable points at:
- \( (-2, 0) \)
- \( (0, 3) \)
- The graph then decreases, crossing the x-axis at \( (3, 0) \), and continues to decrease below the x-axis.
- **Table of \( g(x) \):**
\[
\begin{array}{c|c}
x & g(x) \\
\hline
-3 & -5 \\
-1 & -4 \\
0 & 2 \\
2 & 7 \\
3 & -1 \\
5 & 8 \\
\end{array}
\]
4. **Problems:**
1) Find \( g^{-1}(8) \).
2) Let \( h(x) = 3f(x) - 8g(x) \). Find \( h(-1) \).
3) Find \( f(g(2)) \).
4) \( g(f(5)) \).
----
This transcription and explanation offer a detailed breakdown of the transformations, rate of change, and analysis tasks related to the given functions and graphs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c6a3dff-6729-485c-933e-bf615eefedb6%2F3c93f487-dbd5-45c4-b0bc-e2e3cef6a3be%2Frvcu0if_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
1. **Transformation and Equation Writing:**
Write an equation for the graph of the parent function \( \sqrt{x} \) after it has been horizontally shifted 3 units to the right, shifted down vertically 7 units, and then stretched vertically by a factor of 6.
2. **Average Rate of Change:**
Let \( k(x) = (x + 2)^2 - 5 \). Find the average rate of change of \( k(x) \) between \( x = -3 \) and \( x = 6 \).
3. **Graph and Table Analysis:**
The graph of \( f(x) \) is provided below, along with a table of selected values for the function \( g(x) \).
- **Graph Description:**
The graph of \( f(x) \) is a piecewise linear function with notable points at:
- \( (-2, 0) \)
- \( (0, 3) \)
- The graph then decreases, crossing the x-axis at \( (3, 0) \), and continues to decrease below the x-axis.
- **Table of \( g(x) \):**
\[
\begin{array}{c|c}
x & g(x) \\
\hline
-3 & -5 \\
-1 & -4 \\
0 & 2 \\
2 & 7 \\
3 & -1 \\
5 & 8 \\
\end{array}
\]
4. **Problems:**
1) Find \( g^{-1}(8) \).
2) Let \( h(x) = 3f(x) - 8g(x) \). Find \( h(-1) \).
3) Find \( f(g(2)) \).
4) \( g(f(5)) \).
----
This transcription and explanation offer a detailed breakdown of the transformations, rate of change, and analysis tasks related to the given functions and graphs.
Expert Solution
Step 1
Since you have asked multiple questions in a single request we would be answering only the first question here. In case you want the solutions for the other questions as well please post them separately
To transform the given function as indicated
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