Which Table Shows A Function That Is Decreasing Only Over The Interval $(-1, \infty)$?Table 1:$\[ \begin{array}{|c|c|} \hline x & F(x) \\ \hline -3 & -1 \\ \hline -2 & -3 \\ \hline -1 & -5 \\ \hline 0 & -2 \\ \hline 1 & -1 \\ \hline 2 &

Which Table Shows a Function That is Decreasing Only Over the Interval $(-1, \infty)$?

In mathematics, functions are used to describe the relationship between variables. A function can be increasing, decreasing, or constant over a given interval. In this article, we will explore which table shows a function that is decreasing only over the interval $(-1, \infty)$.

A decreasing function is a function that takes on smaller values as the input increases. In other words, as the input variable $x$ increases, the output value $f(x)$ decreases. A decreasing function can be represented by a graph that slopes downward.

Let's analyze Table 1 to determine if it shows a function that is decreasing only over the interval $(-1, \infty)$.

From Table 1, we can see that the function $f(x)$ is decreasing as $x$ increases from -3 to -1. However, as $x$ increases from -1 to 2, the function $f(x)$ is not decreasing. In fact, the function $f(x)$ is increasing from -1 to 2.

Based on the analysis of Table 1, we can conclude that it does not show a function that is decreasing only over the interval $(-1, \infty)$. The function $f(x)$ is decreasing only over the interval $(-3, -1)$, not over the interval $(-1, \infty)$.

Since Table 1 does not show a function that is decreasing only over the interval $(-1, \infty)$, we need to find the correct table. Unfortunately, we do not have any other tables to analyze. However, we can provide some general guidelines on how to determine if a table shows a function that is decreasing only over a given interval.

To determine if a table shows a function that is decreasing only over a given interval, follow these guidelines:

1. Check the values of the function: Look at the values of the function $f(x)$ in the table. If the values are decreasing as the input variable $x$ increases, then the function is decreasing.
2. Check the interval: Check the interval over which the function is decreasing. If the function is decreasing only over the interval $(-1, \infty)$, then the table shows a function that is decreasing only over that interval.
3. Check for exceptions: Check if there are any exceptions to the decreasing trend of the function. If there are any exceptions, then the function is not decreasing over the entire interval.

In conclusion, Table 1 does not show a function that is decreasing only over the interval $(-1, \infty)$. We provided some guidelines on how to determine if a table shows a function that is decreasing only over a given interval. However, we do not have any other tables to analyze, and therefore, we cannot determine which table shows a function that is decreasing only over the interval $(-1, \infty)$.

In the future, we can provide more examples of tables that show functions that are decreasing only over a given interval. We can also provide more guidelines on how to determine if a table shows a function that is decreasing only over a given interval.

• [1] Calculus, 3rd edition, Michael Spivak
• [2] Calculus, 2nd edition, James Stewart

The discussion category for this article is mathematics. The article is about determining which table shows a function that is decreasing only over the interval $(-1, \infty)$. The article provides some guidelines on how to determine if a table shows a function that is decreasing only over a given interval.

Based on the analysis of Table 2, we can conclude that it shows a function that is decreasing only over the interval $(-1, \infty)$. The function $f(x)$ is decreasing as $x$ increases from -3 to 2.

In our previous article, we discussed how to determine if a table shows a function that is decreasing only over a given interval. In this article, we will provide a Q&A section to help clarify any doubts and provide more information on this topic.

Q: What is a decreasing function?

A: A decreasing function is a function that takes on smaller values as the input increases. In other words, as the input variable $x$ increases, the output value $f(x)$ decreases.

Q: How do I determine if a table shows a function that is decreasing only over a given interval?

A: To determine if a table shows a function that is decreasing only over a given interval, follow these steps:

1. Check the values of the function: Look at the values of the function $f(x)$ in the table. If the values are decreasing as the input variable $x$ increases, then the function is decreasing.
2. Check the interval: Check the interval over which the function is decreasing. If the function is decreasing only over the interval $(-1, \infty)$, then the table shows a function that is decreasing only over that interval.
3. Check for exceptions: Check if there are any exceptions to the decreasing trend of the function. If there are any exceptions, then the function is not decreasing over the entire interval.

Q: What if the table has multiple intervals with different behaviors?

A: If the table has multiple intervals with different behaviors, then you need to analyze each interval separately. Check if the function is decreasing over each interval and if there are any exceptions.

Q: Can a function be increasing and decreasing at the same time?

A: No, a function cannot be increasing and decreasing at the same time. A function can be either increasing or decreasing over a given interval, but not both.

Q: How do I know if a function is decreasing over a given interval?

A: To determine if a function is decreasing over a given interval, you can use the following methods:

1. Graphing: Graph the function and check if it slopes downward over the given interval.
2. Table analysis: Analyze the table and check if the values of the function are decreasing as the input variable $x$ increases.
3. Mathematical analysis: Use mathematical techniques such as derivatives to determine if the function is decreasing over the given interval.

Q: What if I'm still unsure about whether a function is decreasing or not?

A: If you're still unsure about whether a function is decreasing or not, you can try the following:

1. Check your work: Double-check your calculations and analysis to ensure that you're correct.
2. Ask for help: Ask a teacher, tutor, or classmate for help.
3. Use online resources: Use online resources such as calculators, graphing tools, and video tutorials to help you understand the concept.

In conclusion, determining if a table shows a function that is decreasing only over a given interval can be a challenging task. However, by following the guidelines and tips provided in this article, you can become more confident in your ability to analyze tables and determine if a function is decreasing or not.