Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:## Piecewise Functions and Their Values
### Given the following piecewise function:
(Graph Description)
This graph displays a piecewise function composed of line segments and points on a coordinate plane. The x-axis ranges from -7 to 7, and the y-axis ranges from -7 to 7.
**Graph Analysis:**
- The segment from \(x = -7\) to \(x = -6\) is decreasing, transitioning from the point (-7, -3) to (-6, -5).
- From \(x = -6\) to \(x = -3\), the function has a decreasing linear segment, moving from (-6, -5) to (-3, -3).
- The segment between \(x = -3\) and \(x = -2\) is undefined at \(x = -3\) (open circle) and defined at \(x = -2\) with the point (-2, -4).
- For \(x = -2\) to \(x = 2\), the graph is a horizontal line at \(y = -4\).
- From \(x = 2\) to \(x = 3\), there is a jump discontinuity; the function jumps to the point (3, -4) and moves to (3, -5) as indicated by the closed point to open point, respectively.
- The segment from \(x = 3\) to \(x = 5\) is undefined at \(x = 3\) (open circle), and defined through \(x = 5\) at the point (5, -2).
- Finally, there is a line segment increasing from \(x = 5\) to \(x = 6\), ending at the point (6, 5).
### Exercises:
Using the graph, determine the values of the function at specified points.
1. **Find \(f(-4)\):**
2. **Find \(f(2)\):**
*Note: Interpret the graph carefully, examining where the function is defined and how the segments connect.*
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