The Graph Of $f(x) = 3x + 2$ Has A Positive Slope.True Or False: The End Behavior Of The Graph Is That As $x$ Increases, $y$ Decreases, And As $x$ Decreases, $y$ Increases.A. True B. False

Introduction

When analyzing the graph of a linear function, it's essential to understand its end behavior. The end behavior of a graph refers to the behavior of the function as $x$ approaches positive or negative infinity. In this article, we'll explore the end behavior of the graph of $f(x) = 3x + 2$ and determine whether the statement "as $x$ increases, $y$ decreases, and as $x$ decreases, $y$ increases" is true or false.

Understanding the Graph of $f(x) = 3x + 2$

The graph of a linear function in the form $f(x) = mx + b$ is a straight line with a slope of $m$ and a y-intercept of $b$. In the case of $f(x) = 3x + 2$, the slope is $3$ and the y-intercept is $2$. Since the slope is positive, the graph of $f(x) = 3x + 2$ has a positive slope.

End Behavior of the Graph

To determine the end behavior of the graph, we need to consider what happens as $x$ approaches positive or negative infinity. As $x$ increases, the value of $f(x) = 3x + 2$ also increases. This is because the slope of the graph is positive, which means that as $x$ increases, the value of $y$ also increases. Similarly, as $x$ decreases, the value of $f(x) = 3x + 2$ also decreases. This is because the slope of the graph is positive, which means that as $x$ decreases, the value of $y$ also decreases.

Analyzing the Statement

The statement "as $x$ increases, $y$ decreases, and as $x$ decreases, $y$ increases" is a description of the end behavior of the graph. However, based on our analysis, we can see that this statement is incorrect. As $x$ increases, $y$ also increases, and as $x$ decreases, $y$ also decreases.

Conclusion

In conclusion, the graph of $f(x) = 3x + 2$ has a positive slope, and its end behavior is that as $x$ increases, $y$ also increases, and as $x$ decreases, $y$ also decreases. Therefore, the statement "as $x$ increases, $y$ decreases, and as $x$ decreases, $y$ increases" is false.

Final Answer

The final answer is B. False.

Additional Information

• The slope of the graph of $f(x) = 3x + 2$ is $3$, which is a positive value.
• The y-intercept of the graph of $f(x) = 3x + 2$ is $2$.
• As $x$ approaches positive or negative infinity, the value of $f(x) = 3x + 2$ also approaches positive or negative infinity.
• The end behavior of the graph of $f(x) = 3x + 2$ is that as $x$ increases, $y$ also increases, and as $x$ decreases, $y$ also decreases.

Related Topics

• Linear functions
• Graphing linear functions
• End behavior of graphs
• Slope and y-intercept of linear functions

References

• [1] "Graphing Linear Functions" by Math Open Reference
• [2] "End Behavior of Graphs" by Khan Academy
• [3] "Slope and Y-Intercept of Linear Functions" by Purplemath
  

Introduction

In our previous article, we explored the graph of $f(x) = 3x + 2$ and its end behavior. We determined that the graph has a positive slope and that as $x$ increases, $y$ also increases, and as $x$ decreases, $y$ also decreases. In this article, we'll answer some frequently asked questions about the graph of $f(x) = 3x + 2$.

Q&A

Q: What is the slope of the graph of $f(x) = 3x + 2$?

A: The slope of the graph of $f(x) = 3x + 2$ is $3$, which is a positive value.

Q: What is the y-intercept of the graph of $f(x) = 3x + 2$?

A: The y-intercept of the graph of $f(x) = 3x + 2$ is $2$.

Q: As $x$ approaches positive or negative infinity, what happens to the value of $f(x) = 3x + 2$?

A: As $x$ approaches positive or negative infinity, the value of $f(x) = 3x + 2$ also approaches positive or negative infinity.

Q: What is the end behavior of the graph of $f(x) = 3x + 2$?

A: The end behavior of the graph of $f(x) = 3x + 2$ is that as $x$ increases, $y$ also increases, and as $x$ decreases, $y$ also decreases.

Q: Is the graph of $f(x) = 3x + 2$ a function?

A: Yes, the graph of $f(x) = 3x + 2$ is a function because it passes the vertical line test.

Q: Can the graph of $f(x) = 3x + 2$ be described as a linear function?

A: Yes, the graph of $f(x) = 3x + 2$ can be described as a linear function because it is in the form $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How can the graph of $f(x) = 3x + 2$ be graphed?

A: The graph of $f(x) = 3x + 2$ can be graphed by plotting two points on the coordinate plane and drawing a line through them. Alternatively, the graph can be graphed using a graphing calculator or a computer program.

Conclusion

In conclusion, the graph of $f(x) = 3x + 2$ is a linear function with a positive slope and a y-intercept of $2$. As $x$ increases, $y$ also increases, and as $x$ decreases, $y$ also decreases. We hope that this Q&A article has provided you with a better understanding of the graph of $f(x) = 3x + 2$.

Final Answer

The final answer is that the graph of $f(x) = 3x + 2$ is a linear function with a positive slope and a y-intercept of $2$.

Additional Information

• The slope of the graph of $f(x) = 3x + 2$ is $3$, which is a positive value.
• The y-intercept of the graph of $f(x) = 3x + 2$ is $2$.
• As $x$ approaches positive or negative infinity, the value of $f(x) = 3x + 2$ also approaches positive or negative infinity.
• The end behavior of the graph of $f(x) = 3x + 2$ is that as $x$ increases, $y$ also increases, and as $x$ decreases, $y$ also decreases.

Related Topics

• Linear functions
• Graphing linear functions
• End behavior of graphs
• Slope and y-intercept of linear functions

References

• [1] "Graphing Linear Functions" by Math Open Reference
• [2] "End Behavior of Graphs" by Khan Academy
• [3] "Slope and Y-Intercept of Linear Functions" by Purplemath