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.
Look at the graph below and determine whether the function's rate of change is constant or not:
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.
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
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.
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Rate of Change of a Function Represented Graphically
Rate of Change Represented with Steps in the Function's Graph
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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?
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
The problem asks us to determine if the rate of change in the graph is uniform or not. To do this, we need to examine the graph closely to see whether it is linear.
If a graph is linear, it means it is a straight line, indicating a constant (uniform) rate of change. The slope of a straight line does not change, meaning that for every unit increase in there is a proportional and consistent change in .
In contrast, if a graph curves or the line is not straight, the rate of change would not be uniform. This is because a curve indicates that the amount changes for each unit change in is not constant.
By analyzing the given graph, we can see that it is a non-linear function with a visible curve. Since the line is not straight (it appears as a curved line in the graph), the rate of change of the function is not constant across its range.
Therefore, the solution to the problem is that the rate of change is non-uniform.
Consequently, the correct choice, corresponding to a non-uniform rate of change in the graph, is:
Non-uniform
Non-uniform
Given the following graph, determine whether the rate of change is uniform or not
To determine whether the rate of change in the graph is uniform, we must analyze the graph for consistency in slope across its span:
Now, let's work through these steps:
Step 1: By visually inspecting the graph, note that it does not form a perfectly straight line but rather curves upwards. This indicates variability in the slopes along the graph.
Step 2: Since the graph curves, indicating that the slope is not the same throughout, we conclude that the rate of change is not constant.
The curvature implies that the rate of change is non-uniform, as it varies at different points along the x-axis. Therefore, the slope is inconsistent, confirming non-uniformity.
Therefore, the graph shows a non-uniform rate of change.
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
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 function is constant
