Graph the function. Be sure to label three points on the graph. f(x) = ³√x Choose the correct graph below. O A. O B. O C. O D. G
Graph the function. Be sure to label three points on the graph. f(x) = ³√x Choose the correct graph below. O A. O B. O C. O D. G
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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![### Graph the Function: Cubic Root
**Function to Graph:**
\[ f(x) = \sqrt[3]{x} \]
**Instructions:**
Graph the function and label three points on the graph.
**Options:**
- **A.**
- Graph on a grid with axes labeled \( x \) and \( y \).
- A curve is shown passing through the points (-1, -1), (0, 0), and (1, 1).
- **B.**
- Similar to option A, but the curve is incorrectly drawn or oriented.
- **C.**
- Similar to option A, but the curve is oriented incorrectly.
- **D.**
- The curve goes through the correct points with the same orientation as in option A, indicating the cubic root nature, showing points (-1, -1), (0, 0), and (1, 1).
### Details on Diagrams:
**Correct Graph (Option A or D):**
- The graph should show a smooth curve extending from the lower left to the upper right, passing through the origin.
- Points to label:
- \( (-1, -1) \): Point on the curve showing the cubic root of a negative number.
- \( (0, 0) \): The origin, where \( f(x) = 0 \).
- \( (1, 1) \): Point on the curve showing the cubic root of a positive number.
Remember, the cubic root function is symmetric about the origin and smoothly passes through these key points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5176918d-490e-4e4c-9479-7244d7c3ebde%2F7f49e285-71ba-4eb2-a761-b14e11cf12d5%2F2fie6r9_processed.png&w=3840&q=75)
Transcribed Image Text:### Graph the Function: Cubic Root
**Function to Graph:**
\[ f(x) = \sqrt[3]{x} \]
**Instructions:**
Graph the function and label three points on the graph.
**Options:**
- **A.**
- Graph on a grid with axes labeled \( x \) and \( y \).
- A curve is shown passing through the points (-1, -1), (0, 0), and (1, 1).
- **B.**
- Similar to option A, but the curve is incorrectly drawn or oriented.
- **C.**
- Similar to option A, but the curve is oriented incorrectly.
- **D.**
- The curve goes through the correct points with the same orientation as in option A, indicating the cubic root nature, showing points (-1, -1), (0, 0), and (1, 1).
### Details on Diagrams:
**Correct Graph (Option A or D):**
- The graph should show a smooth curve extending from the lower left to the upper right, passing through the origin.
- Points to label:
- \( (-1, -1) \): Point on the curve showing the cubic root of a negative number.
- \( (0, 0) \): The origin, where \( f(x) = 0 \).
- \( (1, 1) \): Point on the curve showing the cubic root of a positive number.
Remember, the cubic root function is symmetric about the origin and smoothly passes through these key points.
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