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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I only need help with D and E, but if the whole problem gets solved that is fine.
![### Consider the Graph of the Function Shown Here
#### Explanation of the Graph
This graph represents a function in the Cartesian coordinate system. The \( x \)-axis ranges from \(-5\) to \(5\) and the \( y \)-axis ranges from \(-5\) to \(5\). The graph depicts various points and lines annotated with their corresponding coordinates. Key points and segments are labeled for clarity:
- The function intersects the y-axis at the point \((-1, 4)\).
- The function has a constant segment between \((-3, 2)\) and \((-1, 2)\).
- It intersects the x-axis at the points \((-3, 0)\) and \((-1, 2)\).
- It continues to go downwards crossing the y-axis and goes beyond \(-5\) on the x-axis.
#### Tasks:
**State the interval(s) over which the function is:**
- (a) Increasing:
- The function is increasing in the interval \( x \in (-3, -1] \).
- (b) Decreasing:
- The function is decreasing in the interval \( x \in (-1, \infty) \).
- (c) Constant:
- The function is constant in the interval \( x \in [-3, -1] \).
**Determine:**
- (d) Domain of the function:
- The domain of the function is \( x \in (-\infty, \infty) \).
- (e) Range of the function:
- The range of the function is \( y \in (-\infty, 4] \).
#### Graph Analysis
The graph shows key features that help us understand the behavior of the function over different intervals. By examining the coordinates and the directions of the graph sections, we can determine where the function is increasing, decreasing, or remaining constant. These aspects are important when analyzing and understanding functions in mathematics.
Visit our educational website for more detailed explanations and resources on graphing functions and analyzing their behavior.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbb4e555-c1ac-4013-a54b-e2091c1d94b2%2Fbda7134e-64b7-48dc-b9fa-7ea208300c9d%2F1v1fme7.jpeg&w=3840&q=75)
Transcribed Image Text:### Consider the Graph of the Function Shown Here
#### Explanation of the Graph
This graph represents a function in the Cartesian coordinate system. The \( x \)-axis ranges from \(-5\) to \(5\) and the \( y \)-axis ranges from \(-5\) to \(5\). The graph depicts various points and lines annotated with their corresponding coordinates. Key points and segments are labeled for clarity:
- The function intersects the y-axis at the point \((-1, 4)\).
- The function has a constant segment between \((-3, 2)\) and \((-1, 2)\).
- It intersects the x-axis at the points \((-3, 0)\) and \((-1, 2)\).
- It continues to go downwards crossing the y-axis and goes beyond \(-5\) on the x-axis.
#### Tasks:
**State the interval(s) over which the function is:**
- (a) Increasing:
- The function is increasing in the interval \( x \in (-3, -1] \).
- (b) Decreasing:
- The function is decreasing in the interval \( x \in (-1, \infty) \).
- (c) Constant:
- The function is constant in the interval \( x \in [-3, -1] \).
**Determine:**
- (d) Domain of the function:
- The domain of the function is \( x \in (-\infty, \infty) \).
- (e) Range of the function:
- The range of the function is \( y \in (-\infty, 4] \).
#### Graph Analysis
The graph shows key features that help us understand the behavior of the function over different intervals. By examining the coordinates and the directions of the graph sections, we can determine where the function is increasing, decreasing, or remaining constant. These aspects are important when analyzing and understanding functions in mathematics.
Visit our educational website for more detailed explanations and resources on graphing functions and analyzing their behavior.
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