We will say that a function is decreasing when, as the value of the independent variable increases, the value of the function decreases.
We will say that a function is decreasing when, as the value of the independent variable increases, the value of the function decreases.
In what domain does the function increase?
Let's assume we have two elements , which we will call and , where the following is true: X1<X2, meaning, X2 is located to the right of X1.
The function is decreasing when: and also .
The function can be decreasing in intervals or throughout its domain.
If you are interested in this article, you might also be interested in the following articles:
Graphical representation of a function
Algebraic representation of a function
Assignment of numerical value in a function
Intervals of increase and decrease of a function
In the blog of Tutorela you will find a variety of articles with interesting explanations about mathematics
Assignment
Find the decreasing area of the function
Solution
coefficient of
Therefore
is the minimum point
The vertex of the function is
The function decreases in the area of
Answer
In what domain is the function negative?
In what domain is the function increasing?
In what domain does the function increase?
Assignment
Given the function in the graph
When is the function positive?
Solution
The intersection point with the axis : is:
First positive, then negative.
Therefore
Answer
Assignment
Given the function in the diagram, what is its domain of positivity?
Solution
Note that the entire function is always above the axis:
Therefore, it will always be positive. Its area of positivity will be for all
Answer
For all
In what interval is the function increasing?
Purple line: \( x=0.6 \)
In what domain does the function increase?
Green line:
\( x=-0.8 \)
In which interval does the function decrease?
Red line: \( x=0.65 \)
Assignment
Given the function in the diagram
What are the areas of positivity and negativity of the function?
Solution
Let's remember that a function is positive when it is above the axis: and the function is negative when it is below the axis
Given that the point of intersection with the axis: is
When it is below:
When it is above:
Therefore, the function is positive when and negative when
Answer
Positive when
Negative when
Assignment
Find the increasing and decreasing area of the function
Solution
In the first step, let's consider that
Therefore and the parabola is at its maximum
In the second step, find of the vertex
according to the data we know
We replace the data in the formula
Then we know that: and we replace it in the function and find that
Answer
Decreasing
Increasing
In which interval does the function decrease?
Red line: \( x=1.3 \)
In what domain does the function increase?
Black line: \( x=1.1 \)
Determine the domain of the following function:
The function describes a student's grades throughout the year.
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.
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.
Always decreasing
Choose the graph that best describes the following:
The acceleration of a ball (Y) after throwing it from a building as a function of time (X).
Since acceleration is dependent on time, it will be constant.
The force of gravity on Earth is constant, meaning the velocity of Earth's gravity is constant and therefore the graph will be straight.
The graph that appears in answer B satisfies this.
Choose the graph that best represents the following:
Temperature of lukewarm water (Y) after placing in the freezer as a function of time (X).
Since the freezing point of water is below 0, the temperature of the water must drop below 0.
The graph in answer B describes a decreasing function and therefore this is the correct answer.
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.
For each number, multiply by.
The function is:
Let's start by assuming that x equals 0:
Now let's assume that x equals minus 1:
Now let's assume that x equals 1:
Now let's assume that x equals 2:
Let's plot all the points on the function graph:
We can see that the function we got is a decreasing function.
Decreasing
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.
For each number, multiply by 0.
The function is:
Let's start by assuming that x equals 0:
Now let's assume that x equals 1:
Now let's assume that x equals -1:
Now let's assume that x equals 2:
Let's plot all the points on the function's graph:
We can see that the function we obtained is a constant function.
Constant