Which graph represents the following piecewise defined function mc003-1.jpg – Delving into the realm of piecewise defined functions, we embark on a journey to unravel the intricacies of the graph mc003-1.jpg. This exploration unveils the significance of graph analysis, revealing the key features and behaviors that define this unique function.
As we traverse the graph’s contours, we uncover the distinct sections that shape its form, each carrying its own mathematical identity. Intercepts, slopes, and asymptotes emerge as guiding markers, illuminating the function’s characteristics.
Piecewise Defined Function mc003-1.jpg
The piecewise defined function mc003-1.jpg is a function that is defined differently for different ranges of input values. The graph of this function can help us visualize how the function behaves for different inputs.
By analyzing the graph, we can identify the different sections of the function and their key features, such as intercepts, slopes, and asymptotes. This information can help us understand the behavior of the function and how it can be used to model different phenomena.
Graph Analysis
The graph of the piecewise defined function mc003-1.jpg consists of three distinct sections:
- For input values less than
- 2, the function is defined as f(x) =
- x + 1. This section of the graph is a line with a slope of
- 1 and a y-intercept of 1.
- For input values between2 and 2, the function is defined as f(x) = x + 1. This section of the graph is a line with a slope of 1 and a y-intercept of 1.
- For input values greater than 2, the function is defined as f(x) =
- x + 5. This section of the graph is a line with a slope of
- 1 and a y-intercept of 5.
Table of Values
The following table shows the input values, corresponding output values, and the section of the graph where each value lies:
| Input Value | Output Value | Section of Graph |
|---|---|---|
| -3 | 4 | Section 1 |
| -1 | 2 | Section 1 |
| 0 | 1 | Section 2 |
| 2 | 3 | Section 2 |
| 3 | 2 | Section 3 |
Equation of the Graph
The equation of the graph for each section of the piecewise defined function is as follows:
- Section 1: f(x) =
x + 1
- Section 2: f(x) = x + 1
- Section 3: f(x) =
x + 5
These equations can be used to determine the output value for any given input value.
Applications, Which graph represents the following piecewise defined function mc003-1.jpg
The piecewise defined function mc003-1.jpg can be used to model a variety of real-world phenomena. For example, it can be used to model the cost of shipping a package, where the cost is different depending on the weight of the package.
It can also be used to model the relationship between the temperature and the amount of heat energy required to raise the temperature by one degree Celsius.
Common Queries: Which Graph Represents The Following Piecewise Defined Function Mc003-1.jpg
What is the purpose of analyzing the graph of mc003-1.jpg?
Graph analysis allows us to identify key features, such as intercepts, slopes, and asymptotes, which provide insights into the function’s behavior and properties.
How does the graph represent the piecewise defined function?
The graph is divided into distinct sections, each corresponding to a different part of the piecewise defined function. The graph’s shape and characteristics reflect the mathematical equations that define the function.
