Given the following graph, determine whether function is constant –9 –9 –9 –8 –8 –8 –7 –7 –7 –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 15 15 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 0 0 0 <path fill="none" stroke="#1565C0" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-opacity=".698" stroke-width="2.5" d="m72.94 884.168.751-7.27.752-7.16.752-7.047.752-6.937.752-6.828.752-6.72.752-6.612.752-6.507.752-6.4.752-6.298.752-6.193.752-6.091.752-5.99.752-5.89.752-5.79.752-5.691.752-5.594.752-5.498.752-5.401.752-5.307.751-5.213.752-5.12.752-5.029 1.504-9.784 1.504-9.426 1.504-9.077 1.504-8.734 1.504-8.398 1.504-8.068 1.504-7.746 1.504-7.431 1.504-7.122 1.503-6.82 1.504-6.523 1.504-6.234 1.504-5.952 1.504-5.674 1.504-5.404 1.504-5.14 3.008-9.511 3.007-8.526 3.008-7.587 3.008-6.693 3.008-5.844 3.008-5.039 6.015-7.827 3.008-2.87 3.008-2.225 3.008-1.62 3.008-1.05 3.007-.516 3.008-.017 3.008.447 3.008.88 6.016 2.931 6.015 4.292 6.016 5.426 6.015 6.347 6.016 7.07 6.016 7.609 6.015 7.976 6.016 8.187 6.016 8.253 6.015 8.187 6.016 8 6.015 7.707 6.016 7.313 6.016 6.836 6.015 6.282 6.016 5.662 6.015 4.987 6.016 4.265 6.016 3.507 6.015 2.718 6.016 1.91 6.016 1.09 6.015.263 6.016-.562 6.015-1.377 6.016-2.178 6.016-2.959 6.015-3.712 6.016-4.434 6.016-5.12 6.015-5.766 6.016-6.366 6.015-6.918 6.016-7.417 6.016-7.864 6.015-8.252 6.016-8.581 6.016-8.85 6.015-9.057 6.016-9.2 6.015-9.278 6.016-9.294 6.016-9.245 6.015-9.133 6.016-8.96 6.016-8.724 6.015-8.43 6.016-8.078 6.015-7.673 6.016-7.214 6.016-6.708 6.015-6.156 6.016-5.564 6.016-4.935 6.015-4.274 6.016-3.587 6.015-2.878 6.016-2.154 6.016-1.423 6.015-.687 6.016.042 6.016.76 6.015 1.456 6.016 2.125 6.015 2.757 6.016 3.342 6.016 3.873 6.015 4.338 6.016 4.728 6.016 5.032 6.015 5.239 6.016 5.339 6.015 5.319 6.016 5.167 6.016 4.871 6.015 4.419 6.016 3.796 6.016 2.99 6.015 1.985 3.008.55 3.008.219 3.008-.142 3.008-.532 3.007-.952 3.008-1.405 3.008-1.89 3.008-2.41 6.015-6.515 6.016-9.019 3.008-5.543 3.008-6.286 3.007-7.069 3.008-7.894 3.008-8.762 3.008-9.675 1.504-5.193 1.504-5.439 1.504-5.69 1.504-5.946 1.503-6.21 1.504-6.479 1.504-6.754 1.504-7.035 1.504-7.323 1.504-7.616 1.504-7.918 1.504-8.224 1.504-8.537 1.504-8.858 1.503-9.185 1.504-9.518 1.504-9.859.752-5.06.752-5.146.752-5.236.752-5.325.752-5.416.752-5.507.752-5.6.752-5.692.752-5.786.752-5.881.752-5.977.752-6.074.752-6.172.752-6.27.752-6.37.752-6.471.751-6.572.752-6.675.752-6.778.752-6.882.752-6.988.752-7.094.752-7.2.752-7.31.752-7.42.752-7.529.752-7.64.752-7.753.752-7.866.752-7.98.752-8.096.752-8.213.752-8.33.752-8.447.752-8.568.752-8.688.752-8.81.751-8.932.752-9.056.752-9.18.752-9.308.752-9.433.752-9.562.752-9.69.752-9.822.752-9.952.376-5.026.376-5.059.376-5.092" paint-order="fill stroke markers">

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 1 1 1 2 2 2 3 3 3 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 –1 –1 –1 1 1 1 2 2 2 3 3 3 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 0 0 0

The graph does not represents a function

Given the following graph, determine whether the rate of change is uniform or not –8 –8 –8 –7 –7 –7 –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 0 0 0

The graph does not represents a function

Look at the graph below and determine whether the function's rate of change is constant or not: –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 0 0

The graph does not represents a function.

Constant Rate of Change

Constant Rate of Change

The meaning of the constant rate of change of a function can be seen when the variables $X$ change in fixed proportions and the $Y$ do as well.

For example, if the constant interval of the $X$ is $2$ and also that of the $Y$ is stable and does not vary from time to time.
The interval of the $Y$ variables does not necessarily have to be equal to that of the $X$ for it to be considered a case of constant rate of change.
If the function is represented with a straight graph, it means that the rate of change is constant.
The rate of change is the slope of the function.

A constant rate of change is represented by a straight line, as seen in the following scheme:

A2 - Constant rate of change of a function

Detailed explanation

Start practice

Test yourself on variation of a function!

Given the following graph, determine whether function is constant

Practice more now

How can one identify the constant rate of change?

Let's see, the rate of change is constant if the following is true:

that when the variable $X$ increases from $4$ to $5$
and the $Y$ increases by $8$

then, when the variable $X$ grows from $102$ to $103$
also the $Y$ increases by $8$

Graph of the constant rate of change

Constant rate of change of a function

Join Over 30,000 Students Excelling in Math!

Endless Practice, Expert Guidance - Elevate Your Math Skills Today

Test your knowledge

Question 1

Given the following graph, determine whether the rate of change is uniform or not

Question 2

Given the following graph, determine whether the rate of change is uniform or not

Question 3

Given the following graph, determine whether the rate of change is uniform or not

Table of Constant Rate of Change

Representation of the function in table

Step graph of the constant rate of change

If you are interested in this article, you might also be interested in the following articles:

Rate of change of a function

Rate of change of a function represented graphically

Rate of change of a function represented by a table of values

Variable rate of change

Rate of change represented with steps in the function's graph

In the blog of Tutorela you will find a variety of articles with interesting explanations about mathematics

Examples and exercises with solutions of constant rate of change

Question 2

Given the following graph, determine whether the rate of change is uniform or not

Question 3

Given the following graph, determine whether the rate of change is uniform or not

Start practice