Drag the points to sketch the graph of the given function. Determine whether f is continuous, piecewise continuous, or neither on the interval 0
Drag the points to sketch the graph of the given function. Determine whether f is continuous, piecewise continuous, or neither on the interval 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Interactive Exercise: Sketching the Graph of a Piecewise Function**
**Instructions:**
Drag the points to sketch the graph of the given function. Determine whether \( f \) is continuous, piecewise continuous, or neither on the interval \( 0 \leq t \leq 3 \).
**Function Definition:**
\[
f(t) =
\begin{cases}
3t^2, & 0 \leq t \leq 1 \\
1 + t, & 1 < t \leq 2 \\
5 - t, & 2 < t \leq 3
\end{cases}
\]
**Graph Explanation:**
The graph below represents the piecewise function \( f(t) \):
- **Interval \( 0 \leq t \leq 1 \):** The function is \( f(t) = 3t^2 \). This forms a parabolic curve starting at the origin (0,0) and ending at the point (1, 3).
- **Interval \( 1 < t \leq 2 \):** The function is \( f(t) = 1 + t \). This is a linear segment starting just above 2 (open circle at \( t = 1 \)) and ending at the point (2, 3).
- **Interval \( 2 < t \leq 3 \):** The function is \( f(t) = 5 - t \). This is another linear segment starting just below 3 (open circle at \( t = 2 \)) and ending at the point (3, 2).
**Visual Features:**
- **Solid Red Circles:** Indicate points of continuity where the function is defined and touches the graph directly.
- **Open Red Circles:** Indicate points where the function is not defined at that specific \( t \), implying a discontinuity at these points.
**Question:**
Using the graph and function properties, decide: \( f(t) \) is \( \_\_\_\_ \).
(Options: Continuous, Piecewise Continuous, Neither)
Explore how the function behaves at different intervals to classify its continuity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bff7fb0-7afb-4d12-af99-7cba91505041%2F20dd53db-4776-4b6a-a6b1-0c38515ca509%2Fixl8kzq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Interactive Exercise: Sketching the Graph of a Piecewise Function**
**Instructions:**
Drag the points to sketch the graph of the given function. Determine whether \( f \) is continuous, piecewise continuous, or neither on the interval \( 0 \leq t \leq 3 \).
**Function Definition:**
\[
f(t) =
\begin{cases}
3t^2, & 0 \leq t \leq 1 \\
1 + t, & 1 < t \leq 2 \\
5 - t, & 2 < t \leq 3
\end{cases}
\]
**Graph Explanation:**
The graph below represents the piecewise function \( f(t) \):
- **Interval \( 0 \leq t \leq 1 \):** The function is \( f(t) = 3t^2 \). This forms a parabolic curve starting at the origin (0,0) and ending at the point (1, 3).
- **Interval \( 1 < t \leq 2 \):** The function is \( f(t) = 1 + t \). This is a linear segment starting just above 2 (open circle at \( t = 1 \)) and ending at the point (2, 3).
- **Interval \( 2 < t \leq 3 \):** The function is \( f(t) = 5 - t \). This is another linear segment starting just below 3 (open circle at \( t = 2 \)) and ending at the point (3, 2).
**Visual Features:**
- **Solid Red Circles:** Indicate points of continuity where the function is defined and touches the graph directly.
- **Open Red Circles:** Indicate points where the function is not defined at that specific \( t \), implying a discontinuity at these points.
**Question:**
Using the graph and function properties, decide: \( f(t) \) is \( \_\_\_\_ \).
(Options: Continuous, Piecewise Continuous, Neither)
Explore how the function behaves at different intervals to classify its continuity.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
