Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
can anyone find f(3) and find when f(x) = 5 on this graph please?
![### Analyzing Piecewise Functions
The provided image is a graph depicting piecewise functions. Let's analyze the components step-by-step for a clear understanding.
#### Graph Components
1. **Axes and Scale**:
- **X-axis** (horizontal scale): The horizontal line represents the X-axis, running from -15 to 15.
- **Y-axis** (vertical scale): The vertical line represents the Y-axis, running from -15 to 15.
- Each grid unit increases by 1 on both the X and Y axes.
2. **Points and Lines**:
- **Closed Circle**: Indicates the endpoint is included in the function. For this graph, we see closed circles at points:
1. (-10, -10)
2. (5, 10)
3. (10, 5)
- **Open Circle**: Indicates the endpoint is not included in the function. For this graph, we see open circles at points:
1. (-8, 0)
2. (5, 5)
3. **Line Segments**:
- **First Line Segment**: Starts from the closed circle at (-10, -10) and extends to the open circle at (-8, 0).
- **Second Line Segment**: Starts from the closed circle at (5, 10) and extends to the open circle at (10, 5).
4. **Arrows**: Indicate that the lines continue infinitely in the specified direction.
- **First Arrow**: From (-15, 5), passing through (-10, -10) and extending downward and leftward.
- **Second Arrow**: From the open circle at (10, 5) and continuing downward and rightward.
#### Function Description
The graph represents a piecewise function with distinct segments. Each segment is active in specific intervals concerning the X-axis:
1. **Segment from (-∞, -10]**:
- The function line extends infinitely from the left (negative infinity) to -10, forming a continuous line segment with a closed circle at (-10, -10).
2. **Segment from [-10, -8)**:
- A line segment is drawn from the closed circle at (-10, -10) to the open circle at (-8, 0).
3. **Segment from [5, 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a15d03a-cf19-479c-9f1f-b178583254bd%2F9a7319ba-bc44-4f7a-84a7-965281637189%2Fujh2ibi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analyzing Piecewise Functions
The provided image is a graph depicting piecewise functions. Let's analyze the components step-by-step for a clear understanding.
#### Graph Components
1. **Axes and Scale**:
- **X-axis** (horizontal scale): The horizontal line represents the X-axis, running from -15 to 15.
- **Y-axis** (vertical scale): The vertical line represents the Y-axis, running from -15 to 15.
- Each grid unit increases by 1 on both the X and Y axes.
2. **Points and Lines**:
- **Closed Circle**: Indicates the endpoint is included in the function. For this graph, we see closed circles at points:
1. (-10, -10)
2. (5, 10)
3. (10, 5)
- **Open Circle**: Indicates the endpoint is not included in the function. For this graph, we see open circles at points:
1. (-8, 0)
2. (5, 5)
3. **Line Segments**:
- **First Line Segment**: Starts from the closed circle at (-10, -10) and extends to the open circle at (-8, 0).
- **Second Line Segment**: Starts from the closed circle at (5, 10) and extends to the open circle at (10, 5).
4. **Arrows**: Indicate that the lines continue infinitely in the specified direction.
- **First Arrow**: From (-15, 5), passing through (-10, -10) and extending downward and leftward.
- **Second Arrow**: From the open circle at (10, 5) and continuing downward and rightward.
#### Function Description
The graph represents a piecewise function with distinct segments. Each segment is active in specific intervals concerning the X-axis:
1. **Segment from (-∞, -10]**:
- The function line extends infinitely from the left (negative infinity) to -10, forming a continuous line segment with a closed circle at (-10, -10).
2. **Segment from [-10, -8)**:
- A line segment is drawn from the closed circle at (-10, -10) to the open circle at (-8, 0).
3. **Segment from [5, 10
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