The rate of change of a function represented by a table of values allows us to compare the variation of the values of (the independent variable of the function) with the variation of the values of (dependent variable of the function). This comparison enables us to determine if the intervals are fixed or not, and, consequently, if the rate of change is constant or not.
Given the following graph, determine whether function is constant
For each we will fill in the corresponding .
We will see at what rate the variables increase in the table.
If the variables grow at the same rate, we can determine that the rate of change of the function is constant.
We will illustrate this topic with the help of two different tables
Representation of the function in table
In this table, the first column represents the variables and the second, the variables according to their correspondence.
If we look closely, we will see that there is a fixed rate that is maintained throughout all the values. For every increase in there is a corresponding increase of in the variables.
Look at the graph below and determine whether the function's rate of change is constant or not:
Given the following graph, determine whether the rate of change is uniform or not
Given the following graph, determine whether the rate of change is uniform or not
Table representation of a function with a non-constant rate of change
Also in this table, the first column represents the variables and the second the variables according to their correspondence.
If we look closely, we will see that in this case there is no fixed rate that remains stable across all values.
If you are interested in this article, you might also be interested in the following articles:
Rate of Change of a Function Represented Graphically
Rate of Change Represented with Steps in the Function's Graph
On the Tutorela blog, you will find a variety of articles with interesting explanations about mathematics
Given the following graph, determine whether the rate of change is uniform or not?
Let's remember that if the function is not a straight line, its rate of change is not uniform.
Since the graph is not a straight line - the rate of change is not uniform.
Non-uniform
Given the following graph, determine whether the rate of change is uniform or not
Let's remember that if the function is not a straight line, its rate of change is not uniform.
Since the graph is not a straight line - the rate of change is not uniform.
Non-uniform
Look at the graph below and determine whether the function's rate of change is constant or not:
First we need to remember that if the function is not a straight line, its rate of change is not constant.
The rate of change is not uniform since the function is not a straight line.
Not constant
Given the following graph, determine whether the rate of change is uniform or not
The problem requires us to determine whether the rate of change in a given graph is uniform.
A uniform rate of change corresponds to a constant slope, which is characteristic of a linear graph. First, we'll examine the graphical representation.
Upon observing the graph, we see that it displays a straight horizontal line. A horizontal line on a graph indicates that for any two points and , the difference in -values is zero, i.e., . This implies that the slope, given by the formula , is zero and remains constant as we move along the line.
Because the line is horizontal and does not change its slope throughout, the rate of change is indeed uniform across the entire graph.
Therefore, the rate of change is uniform.
Uniform
Given the following graph, determine whether the rate of change is uniform or not?
Remember that if the function is a straight line, its rate of change will be constant.
Due to the fact that the graph is a straight line - the rate of change is constant.
Uniform
Given the following graph, determine whether the rate of change is uniform or not
Given the following graph, determine whether the rate of change is uniform or not
Given the following graph, determine whether the rate of change is uniform or not
