Increasing and Decreasing Intervals of a Function: Drawing conclusions from a table or graph

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x < 2$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x < 2$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x < 0$X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

$x < 0$

Let's remember that a function is increasing if both $x$ values and $y$ values are increasing simultaneously.

A function is decreasing if $x$ values are increasing while $y$ values are decreasing simultaneously.

According to the value table, we can see that in the domain $x < 2$, the$x$ values are increasing while the $y$ values are decreasing simultaneously. Therefore, the function is decreasing in the domain $x < 2$.

To solve this problem, we'll examine each interval provided between the points for $f(x)$ from the graph, checking where $\ f(x)$ decreases:

• Step 1: Look at the interval $2 < x < 3$.
  - For $x = 2$, $\ f(x) = 15$ and for $x = 3$, $\ f(x) = 0$.
  - Since $15 \to 0$ as $x$ moves from 2 to 3, the function decreases. Thus, this interval is decreasing.
• Step 2: Examine the interval $x > 3.5$.
  - For $x = 3.5$, $\ f(x) = 2$ at the starting point, and it decreases beyond this point.
  - Since we need to find where $f(x)$ decreases, and the function decreases as it's moving towards a lower value from this point, this indeed indicates a decreasing domain.

Therefore, the intervals where the function decreases are $2 < x < 3$ and $x > 3.5$.

The solution to this problem is that Answers B and C are correct, identifying the domains where $f(x)$ decreases.

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$10 > x > 0$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$10 > x > 0$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x > 0$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x > 0$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x > 3$X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

$x > 3$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x < -2$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x < -2$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to our given value table, we can see that X values increase while Y values decrease simultaneously.

Therefore, the function decreases throughout its domain, and there is no domain where it increases.

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$0 > x$X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x > 0$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$1.5 > x > 0$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$1.5 > x > 0$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x < 0$X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

$x < 0$

Note that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$2.5 > x > 0$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$2.5 > x > 0$

Note that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x < 3$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x < 3$

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where$x > -0.5$the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x > -0.5$