Consider the following function. g(x) = 3 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**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: [____]**

- **Vertical separation: [____]**

**Graph Explanation:**

The graph is a standard Cartesian coordinate grid with both x and y axes ranging from -10 to 10. The function appears to introduce line segments via the floor function applied to \( \frac{x}{4} \) and scaled by a factor of 3, which means it will create step-like lines on the graph.

**Key Features to Identify:**

- **Axes:** The x-axis and y-axis are labeled, with increments marked at every unit.
- **Grid Lines:** The graph is covered with a grid for easier reading and plotting of points.
- **Function Behavior:** As \( x \) increases, \( \left\lfloor \frac{x}{4} \right\rfloor \) will yield constant values for intervals of length 4, creating horizontal line segments on the plot with a vertical step every 4 units in \( x \). Each segment represents one such interval. 

The task is to calculate the horizontal length of each segment of constant function value and find the vertical separation between successive horizontal line segments.
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: [____]** - **Vertical separation: [____]** **Graph Explanation:** The graph is a standard Cartesian coordinate grid with both x and y axes ranging from -10 to 10. The function appears to introduce line segments via the floor function applied to \( \frac{x}{4} \) and scaled by a factor of 3, which means it will create step-like lines on the graph. **Key Features to Identify:** - **Axes:** The x-axis and y-axis are labeled, with increments marked at every unit. - **Grid Lines:** The graph is covered with a grid for easier reading and plotting of points. - **Function Behavior:** As \( x \) increases, \( \left\lfloor \frac{x}{4} \right\rfloor \) will yield constant values for intervals of length 4, creating horizontal line segments on the plot with a vertical step every 4 units in \( x \). Each segment represents one such interval. The task is to calculate the horizontal length of each segment of constant function value and find the vertical separation between successive horizontal line segments.
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