Where is the Function Increasing, Decreasing, and Constant?

Find Where the Function is Increasing, Decreasing, and Constant - How it Works - Video

Increasing, Decreasing, Constant Chart

Increasing, Decreasing, Constant Chart:

When determining whether the function is increasing, decreasing, or constant, we look at the output values. We always go left to right, when we pick two points.

The function is increasing when the output of the second point is greater than the output of the first point.

The function is decreasing when the output of the second point is smaller than the output of the first point.

The function is constant when the output of the second point is equal to than the output of the first point.

Example 1

Example 1:

When we determining where the graph increases, decrease, and/or constant, we have to separate the graph into sections. Each time a "turn" we have a section. Sometimes this "turn" is a corner and sometimes the "turn" is an extrema.

Here we a minimum at (0, -3). We look at the output values to determine if the graph is increasing, decreasing, and/or constant. We pick two points and the second point is always to the right of the first point.

In the red section, our output values are 3.25 then 1. Since the output value of our second point is less than output value of our first point, our graph is decreasing in that section. To write our answer we can use interval notation, (-∞, 0].

In the orangish section, our output values are 2.06 then 4.56. Since the output value of our second point is greater than output value of our first point, our graph is increasing in that section. To write our answer we can use interval notation, [0, +∞).

We included 0 in both answers by using brackets instead of a parenthesis because it is true for both sections.

We don't have any constant sections in this graph.

Example 2

Example 2:

When we determining where the graph increases, decrease, and/or constant, we have to separate the graph into sections. Each time a "turn" we have a section. Sometimes this "turn" is a corner and sometimes the "turn" is an extrema.

Here we a maximum at (0, 4). We look at the output values to determine if the graph is increasing, decreasing, and/or constant. We pick two points and the second point is always to the right of the first point.

In the red section, our output values are 2.65 then 3.46. Since the output value of our second point is greater than output value of our first point, our graph is increasing in that section. To write our answer we can use interval notation, [-4, 0].

In the orangish section, our output values are 3.87 then 3.12. Since the output value of our second point is less than output value of our first point, our graph is decreasing in that section. To write our answer we can use interval notation, [0, 4].

We included 0 in both answers by using brackets instead of a parenthesis because it is true for both sections.

We also don't have any constant sections in this graph.

Example 3

Example 3:

When we determining where the graph increases, decrease, and/or constant, we have to separate the graph into sections. Each time a "turn" we have a section. Sometimes this "turn" is a corner and sometimes the "turn" is an extrema.

Here we don't have any extrema, but we have "turns". In this example the turns are not connect. So we have three sections. Once again, we look at the output values to determine if the graph is increasing, decreasing, and/or constant. We pick two points and the second point is always to the right of the first point.

In the red section, our output values are -5 then -4. Since the output value of our second point is greater than output value of our first point, our graph is increasing in that section. To write our answer we can use interval notation, (-∞, -1). -1 has a parenthesis because -1 is not included in this section.

In the blue section, our output values are 2 then 2. Since the output value of our second point is the same as our output value of our first point, our graph is constant in that section. To write our answer we can use interval notation, [-1, 3). -1 has a bracket because -1 is included in this section, and 3 has a parenthesis, because it is not included in this section.

In the orangish section, our output values are 0.5 then -0.8. Since the output value of our second point is less than output value of our first point, our graph is decreasing in that section. To write our answer we can use interval notation, [3, +∞). 3 has a bracket because 3 is included in this section.

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