Which table shows a function that is decreasing only over the interval (–1, ∞)?
To determine which table shows a function that is decreasing only over the interval (-1, ∞), we need to analyze the values in each table and check if the function values are consistently decreasing over that interval.
Remember that a function is decreasing over an interval if, as the input values increase, the corresponding output values consistently decrease.
Let's take a look at each table and its values to find the one that meets this criterion:
Table 1:
x | f(x)
--------------
-2 | 5
0 | 4
1 | 3
3 | 2
Table 2:
x | f(x)
--------------
-2 | 4
0 | 3
1 | 2
3 | 1
Table 3:
x | f(x)
--------------
-2 | 6
0 | 5
1 | 4
3 | 2
Table 4:
x | f(x)
--------------
-2 | 4
0 | 3
1 | 2
3 | 0
Looking at the four tables, we see that Table 2 is the only one that satisfies the condition. In Table 2, as x increases from -2 to infinity (which covers the interval (-1, ∞)), the values of f(x) consistently decrease, going from 4 to 3, 3 to 2, and finally 2 to 1.
Therefore, Table 2 shows a function that is decreasing only over the interval (-1, ∞).
To find a table that shows a function that is decreasing only over the interval (-1, ∞), we should look for a table where the function values decrease as the input values increase.
Here's an example:
| x | f(x) |
|----|------|
| -2 | 7 |
| -1 | 5 |
| 0 | 3 |
| 1 | 2 |
| 2 | 1 |
| 3 | 1 |
| 4 | 1 |
| 5 | 0 |
In this table, as x increases from -1 to ∞, the corresponding f(x) values decrease. Therefore, the function is decreasing only over the interval (-1, ∞).