Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if there is one; e. the following function values. f(-1) f(4)
Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if there is one; e. the following function values. f(-1) f(4)
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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![**Title: Analyzing Graphs of Functions**
**Instructions:**
Use the graph to determine:
a. The function's domain;
b. The function's range;
c. The x-intercepts, if any;
d. The y-intercept, if there is one;
e. The following function values:
- \( f(-1) \)
- \( f(4) \)
**Graph Analysis:**
The graph provided is a piecewise function plotted on a Cartesian plane. The diagram shows a blue line segment connecting points that give an insight into the behavior and properties of the function.
**Graph Details:**
- **X-axis:** Spanning from -2 to 8 with intervals of 1.
- **Y-axis:** Spanning from -5 to 5 with intervals of 1.
- The function appears to be composed of two linear segments:
- The first segment starts from (-2, -4) to (2, 0).
- The second segment starts from (2, 0) to (6, 2).
**Tasks:**
**a. What is the domain?**
**Answer:**
The domain of a function is the set of all possible input values (x-values) for which the function is defined. Based on the graph, the x-values range from -2 to 6.
- Domain: \([-2, 6]\)
**b. What is the range?**
**Answer:**
The range of a function is the set of all possible output values (y-values) corresponding to the domain. Based on the graph, the y-values range from -4 to 2.
- Range: \([-4, 2]\)
**c. What are the x-intercepts?**
**Answer:**
The x-intercepts are the points where the graph crosses the x-axis (y=0). From the graph, the x-intercept occurs at x = 2.
- X-intercepts: \(x = 2\)
**d. What is the y-intercept?**
**Answer:**
The y-intercept is the point where the graph crosses the y-axis (x=0). From the graph, the y-intercept occurs at (0, -2).
- Y-intercept: \( (0, -2) \)
**e. Determine the following function values:**
- \( f(-1) \):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fee617b-deaa-4a69-bacc-ab70232246e7%2F55ce6dd0-cbcc-4dcb-b3d4-72c47bf730e8%2Fa3506ci_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing Graphs of Functions**
**Instructions:**
Use the graph to determine:
a. The function's domain;
b. The function's range;
c. The x-intercepts, if any;
d. The y-intercept, if there is one;
e. The following function values:
- \( f(-1) \)
- \( f(4) \)
**Graph Analysis:**
The graph provided is a piecewise function plotted on a Cartesian plane. The diagram shows a blue line segment connecting points that give an insight into the behavior and properties of the function.
**Graph Details:**
- **X-axis:** Spanning from -2 to 8 with intervals of 1.
- **Y-axis:** Spanning from -5 to 5 with intervals of 1.
- The function appears to be composed of two linear segments:
- The first segment starts from (-2, -4) to (2, 0).
- The second segment starts from (2, 0) to (6, 2).
**Tasks:**
**a. What is the domain?**
**Answer:**
The domain of a function is the set of all possible input values (x-values) for which the function is defined. Based on the graph, the x-values range from -2 to 6.
- Domain: \([-2, 6]\)
**b. What is the range?**
**Answer:**
The range of a function is the set of all possible output values (y-values) corresponding to the domain. Based on the graph, the y-values range from -4 to 2.
- Range: \([-4, 2]\)
**c. What are the x-intercepts?**
**Answer:**
The x-intercepts are the points where the graph crosses the x-axis (y=0). From the graph, the x-intercept occurs at x = 2.
- X-intercepts: \(x = 2\)
**d. What is the y-intercept?**
**Answer:**
The y-intercept is the point where the graph crosses the y-axis (x=0). From the graph, the y-intercept occurs at (0, -2).
- Y-intercept: \( (0, -2) \)
**e. Determine the following function values:**
- \( f(-1) \):
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