We will say that a function is increasing when, as the value of the independent variable increases, the value of the function increases.
We will say that a function is increasing when, as the value of the independent variable increases, the value of the function increases.
In what domain does the function increase?
For example
let's assume we have two elements , which we will call and , where the following is true: , that is, is located to the right of .
The function is increasing when and also .
The function can be increasing in intervals or can be continuous throughout its domain.
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Domain of a function
Indefinite integral
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Variation of a function
Decreasing function
Constant function
Functions for seventh grade
Intervals of increase and decrease of a function
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Assignment
Find the increasing area of the function
Solution
Solve the equation using the shortcut multiplication formula
From this, the data we have are:
Find the vertex using the formula
Vertex point is
From this we know that:
And therefore the function is maximum
The function is increasing 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 linear function in the graph.
When is the function positive?
Solution
The function is positive when it is above the axis:
Intersection point with the axis: is
According to the graph the function is positive
therefore
Answer
Assignment
Find the increasing area of the function
Solution
Solve the equation using the shortcut multiplication formula
From this, the data we have are:
Find the vertex by the formula
The vertex point is
From this we know that:
Therefore the function is maximum
The function is increasing in the area of
Answer
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
Find the increasing area of the function
Solution
Solve the equation using the shortcut multiplication formula
From this, the data we have are:
Find the vertex using the formula
The vertex point
From this we know that
Therefore, the function is maximum
The function is increasing from
Answer
Assignment
Find the increasing area of the function
Solution
Solve the equation using the shortcut multiplication formula
From this, the data we have are:
Find the vertex by the formula
Now replace in the given function
The vertex point is
From this we know that:
Therefore, the function is minimum
The function increases in the area of
Answer
In which interval does the function decrease?
The red line \( x=1.3 \)
In what area 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.