The 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.
In what domain does the function increase?
Determine in which domain the function is negative?
In what domain is the function increasing?
In what domain does the function increase?
In what interval is the function increasing?
Purple line: \( x=0.6 \)
In what domain does the function increase?
Let's remember that the function increases if the values and values increase simultaneously.
On the other hand, the function decreases if the values increase while the 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 values are increasing.
x > 0
Determine in which domain the function is negative?
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.
x > 1
In what domain is the function increasing?
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.
All values of
In what domain does the function increase?
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.
x<0
In what interval is the function increasing?
Purple line:
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.
x<0.6
Does the function in the graph decrease throughout?
Is the function in the graph decreasing?
Is the function shown in the graph below decreasing?
Is the function in the graph decreasing?
Is the function shown in the graph below decreasing?
Does the function in the graph decrease throughout?
To solve this problem, we'll begin by examining the graph of the function provided:
Upon inspecting the graph, we find:
- There are sections where the function's y-values appear to remain constant or potentially rise as the x-values increase. Specifically, even if the function decreases in major portions, any interval where it doesn't means the function cannot be classified as decreasing throughout.
Thus, the function does not strictly decrease on the entire interval shown. Therefore, the solution to the problem is No.
No
Is the function in the graph decreasing?
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: By examining the graph, the red line starts at a higher point on the y-axis and moves downward to a lower point as it moves horizontally across the x-axis from left to right.
Step 2: Since for every point, the red line descends as it progresses from the leftmost point to the rightmost, this indicates a consistent decrease in the y-values.
Therefore, the solution to the problem is Yes, the function in the graph is decreasing.
Yes
Is the function shown in the graph below decreasing?
The graph presented is a straight line. To determine whether the function is decreasing, we need to examine the slope of this line.
The line has a negative slope, as it moves downward from left to right. A function is considered decreasing when its slope is negative.
In formal terms, for a linear function expressed as , if the slope is negative, the function is decreasing over its entire domain.
From the graph, it's evident that the line has a negative slope, thus indicating that the function is indeed decreasing.
Therefore, the answer to the problem is Yes.
Yes
Is the function in the graph decreasing?
To analyze whether the function in the graph is decreasing, we must understand how the function's behavior is defined by its graph:
Therefore, the function represented by the graph is not decreasing.
No
Is the function shown in the graph below decreasing?
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Observing the graph, the function's graph is a line moving from the top left to the bottom right. This indicates it slopes downward as we move from left to right across the -axis.
Step 2: According to the definition of a decreasing function, for any , it must hold true that . Since the graph shows a line moving downward, this condition is satisfied throughout its domain.
Therefore, the function represented by the graph is indeed decreasing.
The final answer is Yes.
Yes
In which domain does the function increase?
Green line:
\( x=-0.8 \)
In which interval does the function decrease?
Red line: \( x=0.65 \)
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.
Which domain corresponds to the described function:
The function represents the velocity of a stone after being dropped from a great height as a function of time.
In which domain does the function increase?
Green line:
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.
All values of
In which interval does the function decrease?
Red line:
Remember that a function is increasing if both the values and the values are increasing simultaneously.
A function is decreasing if the values are increasing while the 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 .
All values of
In what domain does the function increase?
Black line:
Remember that a function is increasing if the values and 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 values are increasing.
1.1 > x > 0
Determine the domain of the following function:
The function describes a student's grades throughout the year.
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.
Impossible to know.
Which domain corresponds to the described function:
The function represents the velocity of a stone after being dropped from a great height as a function of time.
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.
Always increasing