Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function. h(x)=√x+1 Choose the correct graph below. O A. -12 12- - 12² Q Find the domain of h(x). (Type your answer in interval notation.) Find the range of h(x). П (Type your answer in interval notation.) O B. -12 12- 12 Q O C. Q 12- Ja -12 O D. -12 12- -12 Q Ау 12- y=√x * -12 -123 Q
Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function. h(x)=√x+1 Choose the correct graph below. O A. -12 12- - 12² Q Find the domain of h(x). (Type your answer in interval notation.) Find the range of h(x). П (Type your answer in interval notation.) O B. -12 12- 12 Q O C. Q 12- Ja -12 O D. -12 12- -12 Q Ау 12- y=√x * -12 -123 Q
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Educational Content: Graphing Functions and Finding Domain and Range
#### Instructions:
Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function.
#### Function:
\[ h(x) = \sqrt{x} + 1 \]
#### Visual Explanation of Graphs:
- **Basic Graph Provided:** The graph of the basic function \( y = \sqrt{x} \) is given. This graph starts at the origin (0,0) and curves upwards to the right along the x-axis.
#### Task:
Choose the correct graph below that represents \( h(x) = \sqrt{x} + 1 \).
#### Options:
- **Graph A:** Shifts the graph of \( y = \sqrt{x} \) up by 1 unit.
- **Graph B:** Incorrect shift or transformation.
- **Graph C:** Incorrect shift or transformation.
- **Graph D:** Incorrect shift or transformation.
#### Concept Check:
When transforming the graph of \( y = \sqrt{x} \) to \( h(x) = \sqrt{x} + 1 \), observe the vertical shift upwards due to the addition of 1.
#### Domain and Range:
- **Find the domain of \( h(x) \):**
\[ \text{(Type your answer in interval notation.)} \]
- **Find the range of \( h(x) \):**
\[ \text{(Type your answer in interval notation.)} \]
### Graph Interpretation:
- **Axes Details:** Each graph has x and y axes scaled from -12 to 12.
- **Arrows and Points:** Evaluate each graph to determine how the function is shifted or transformed from the basic graph.
Use these elements to correctly determine the graph and the domain and range of the function \( h(x) = \sqrt{x} + 1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5176918d-490e-4e4c-9479-7244d7c3ebde%2F293ef214-89b6-4044-af5d-e1af85fe3167%2Fj57ss1s_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Content: Graphing Functions and Finding Domain and Range
#### Instructions:
Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function shown to the right. Find the domain and range of the function.
#### Function:
\[ h(x) = \sqrt{x} + 1 \]
#### Visual Explanation of Graphs:
- **Basic Graph Provided:** The graph of the basic function \( y = \sqrt{x} \) is given. This graph starts at the origin (0,0) and curves upwards to the right along the x-axis.
#### Task:
Choose the correct graph below that represents \( h(x) = \sqrt{x} + 1 \).
#### Options:
- **Graph A:** Shifts the graph of \( y = \sqrt{x} \) up by 1 unit.
- **Graph B:** Incorrect shift or transformation.
- **Graph C:** Incorrect shift or transformation.
- **Graph D:** Incorrect shift or transformation.
#### Concept Check:
When transforming the graph of \( y = \sqrt{x} \) to \( h(x) = \sqrt{x} + 1 \), observe the vertical shift upwards due to the addition of 1.
#### Domain and Range:
- **Find the domain of \( h(x) \):**
\[ \text{(Type your answer in interval notation.)} \]
- **Find the range of \( h(x) \):**
\[ \text{(Type your answer in interval notation.)} \]
### Graph Interpretation:
- **Axes Details:** Each graph has x and y axes scaled from -12 to 12.
- **Arrows and Points:** Evaluate each graph to determine how the function is shifted or transformed from the basic graph.
Use these elements to correctly determine the graph and the domain and range of the function \( h(x) = \sqrt{x} + 1 \).
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