Determine the domain of the following function: The function represents the weight of a person over a period of 3 years.

Partly increasing and partly decreasing.

Determine which domain corresponds to the function described below: The function represents the amount of fuel in a car's tank according to the distance traveled by the car.

Partly increasing and partly decreasing

Determine which domain corresponds to the function described below: The function represents the height of a child from birth to first grade.

Partly increasing and partly decreasing.

Determine which domain corresponds to the described function: The function represents the amount of water in a pool while it is being filled.

Partly increasing and partly decreasing.

Increasing Intervals of a function

The increasing intervals of a function

An increasing interval of a function expresses the same values of X (the interval), in which the values of the function (Y) grow parallel to the growth of the values of X to the right.

In certain cases, the increasing interval begins at the minimum point, but it does not necessarily have to be this way.

Detailed explanation

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Test yourself on increasing and decreasing intervals of a function!

Does the function in the graph decrease throughout?

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Examples and exercises with solutions of intervals of increasing functions

Exercise #1

In what domain does the function increase?

Video Solution

Step-by-Step Solution

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.

Answer

$x > 0$

Exercise #2

In what domain is the function negative?

Video Solution

Step-by-Step Solution

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.

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

Answer

$x > 1$

Exercise #3

In what domain is the function increasing?

Video Solution

Step-by-Step Solution

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.

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

Answer

Entire $x$

Exercise #4

In what domain does the function increase?

Video Solution

Step-by-Step Solution

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.

Answer

$x<0$

Exercise #5

In what interval is the function increasing?

Purple line: $x=0.6$

Video Solution

Step-by-Step Solution

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.

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

Answer

$x<0.6$

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Question 1

Is the function in the graph decreasing?

Question 2

Is the function shown in the graph below decreasing?

Question 3

Is the function in the graph decreasing?

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