Increasing and Decreasing Intervals of a Function - Examples, Exercises and Solutions

Let's first remember that a function is increasing if both the X and Y values are increasing simultaneously.

Conversely, a function is decreasing if the X values are increasing while the Y values are decreasing simultaneously.

In the graph shown, we can see that the function is increasing in every domain and therefore the function is increasing for all values of X.

Let's remember that a function is described as 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.

In the graph, we can see that in the domain x < 0.6 the function is increasing, meaning the Y values are increasing.

Let's remember that the function increases if the $x$ values and $y$ values increase simultaneously.

On the other hand, the function decreases if the $x$ values increase while the $y$ values decrease simultaneously.

In the given graph, we can see that the function increases in the domain where x > 0 ; in other words, where the $y$ values are increasing.

Let's remember that the function increases if the X values and Y values increase simultaneously.

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

In the given graph, we notice that the function increases in the domain where x < 0 , meaning the Y values are increasing.

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.

In the graph, we can observe that in the domain x > 1 the function is decreasing, meaning the Y values are decreasing.

According to logic, a child's height from birth until first grade will always be increasing as the child grows.

Therefore, the domain that suits this function is - always increasing.

According to logic, the computer's battery during use will always decrease since the battery serves as an energy source for the computer.

Therefore, the domain that suits this function is - always decreasing.

According to logic, the speed of the stone during a fall from a great height will increase as it falls with acceleration.

In other words, the speed of the stone increases, so the appropriate domain for this function is - always increasing.

According to logic, the student's grades throughout the year depend on many criteria that are not given to us.

Therefore, the appropriate domain for the function is - it is impossible to know.

According to the definition, the amount of fuel in the car's tank will always decrease, since during the trip the car consumes fuel in order to travel.

Therefore, the domain that is suitable for this function is - always decreasing.

Logically, a person's energy level throughout the day changes and depends on many factors.

On one hand, energy levels rise for example when a person eats or consumes caffeine.

On the other hand, energy levels drop when for example a person moves a lot or exercises.

Therefore, the domain that fits this function is - partly increasing and partly decreasing.

Logically, a person's weight is something that fluctuates.

In one week, a person's weight can increase, but in the following week, it can decrease.

Therefore, the domain that suits this function is - partly increasing and partly decreasing.

Remember that a function is increasing if both the $x$ values and the $y$ values are increasing simultaneously.

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

In the graph we can see that the function is decreasing in all domains. In other words, it is decreasing for all $x$.

Remember that a function is increasing if the $x$ values and $y$ values are increasing simultaneously.

A function is decreasing if the X values are increasing and the Y values are decreasing simultaneously.

In the plotted graph, we can see that in the domain 1.1 > x > 0 the function is increasing—meaning the $y$ values are increasing.

The function increases if X values and Y values increase simultaneously.
In this function, despite its unusual form, we can observe that the function continues to increase according to the definition at all times,
Furthermore there is no stage where the function decreases.
Therefore, we can say that the function increases for all X, there is no X we can input where the function will be decreasing.