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.

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 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? –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 represent 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 –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 –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 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 –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 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

Variation of a Function - Examples, Exercises and Solutions

Understanding Variation of a Function

Complete explanation with examples

The variation of a function means the rate at which a certain function changes. The rate of variation of a function is also called the slope.

According to the mathematical definition, the slope represents the change of the function $(Y)$ by increasing the value of $X$ by $1$ .

If the function's graph is represented by a straight line, it means that the rate of variation of the function is constant
However, if the graph is not represented by a straight line, this implies that the rate of variation of the function is not constant

Detailed explanation

Practice Variation of a Function

Test your knowledge with 9 quizzes

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

Examples with solutions for Variation of a Function

Step-by-step solutions included

Exercise #1

Look at the graph below and determine whether the function's rate of change is constant or not:

Step-by-Step Solution

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.

Answer:

Not constant

Video Solution

Exercise #2

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

Step-by-Step Solution

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.

Answer:

Non-uniform

Video Solution

Exercise #3

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

Step-by-Step Solution

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.

Answer:

Non-uniform

Video Solution

Exercise #4

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

Step-by-Step Solution

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.

Answer:

Uniform

Video Solution

Exercise #5

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

Step-by-Step Solution

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 $x$ there is a proportional and consistent change in $y$ .

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 $y$ changes for each unit change in $x$ 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

Answer:

Non-uniform

Video Solution

Continue Your Math Journey

Master Variation of a Function first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Rate of Change of a Function Rate of change represented with steps in the graph of the function Rate of change of a function represented graphically Constant Rate of Change Variable Rate of Change Rate of Change of a Function Represented by a Table of Values Functions for Seventh Grade Increasing and Decreasing Intervals (Functions)Increasing functions Decreasing function Constant Function Decreasing Interval of a function Increasing Intervals of a function Domain of a Function Indefinite integral Inputing Values into a Function

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Calculate the rate of change from an equation Calculate the rate of change from a table Calculate the rate of change in a graph Drawing conclusions from a table or graph

Variation of a Function - Examples, Exercises and Solutions

Understanding Variation of a Function

Practice Variation of a Function

Examples with solutions for Variation of a Function

More Variation of a Function Questions