Consider the following function. g(x) = 3[4] Step 2 of 2: Find the length of the individual line segments of this function. Then, find the positive vertical separation between line segment. Simplify your answer. Answer Length: Vertical separation: 10 --5 10 5 -S -10 Enable Zoom/Pan XA 10 Keyboard
Consider the following function. g(x) = 3[4] Step 2 of 2: Find the length of the individual line segments of this function. Then, find the positive vertical separation between line segment. Simplify your answer. Answer Length: Vertical separation: 10 --5 10 5 -S -10 Enable Zoom/Pan XA 10 Keyboard
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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Question
![**Consider the following function.**
\[ q(x) = 3 \left\lfloor \frac{x}{4} \right\rfloor \]
**Step 2 of 2:** Find the length of the individual line segments of this function. Then, find the positive vertical separation between each line segment. Simplify your answer.
**Answer:**
- **Length:** [Text box for input]
- **Vertical separation:** [Text box for input]
**Graph Explanation:**
The graph represents the function \( q(x) = 3 \left\lfloor \frac{x}{4} \right\rfloor \) plotted on a coordinate plane with \( x \) and \( y \) axes ranging from -10 to 10. The grid lines indicate units by ones, and the axes are marked at key intervals (e.g., -5, 0, 5).
The function is a step function, characterized by horizontal line segments that occur at each integer step of \( x/4 \), and the height of each step is determined by multiplying 3 with the floor function value of \( x/4 \). Vertical separations are the differences in \( y \)-values between consecutive steps, and need to be calculated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4118575d-179e-4f1c-8fc7-fc378f435f9b%2F1124051b-f56a-4d3c-b7ff-1307cd818afd%2F5ppyux8_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following function.**
\[ q(x) = 3 \left\lfloor \frac{x}{4} \right\rfloor \]
**Step 2 of 2:** Find the length of the individual line segments of this function. Then, find the positive vertical separation between each line segment. Simplify your answer.
**Answer:**
- **Length:** [Text box for input]
- **Vertical separation:** [Text box for input]
**Graph Explanation:**
The graph represents the function \( q(x) = 3 \left\lfloor \frac{x}{4} \right\rfloor \) plotted on a coordinate plane with \( x \) and \( y \) axes ranging from -10 to 10. The grid lines indicate units by ones, and the axes are marked at key intervals (e.g., -5, 0, 5).
The function is a step function, characterized by horizontal line segments that occur at each integer step of \( x/4 \), and the height of each step is determined by multiplying 3 with the floor function value of \( x/4 \). Vertical separations are the differences in \( y \)-values between consecutive steps, and need to be calculated.
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