Rate of change of a function represented graphically - Examples, Exercises and Solutions

Rate of Change of a Function Represented Graphically

The rate of change of a function represented graphically allows us to determine in a much more intuitive way whether it is a constant (fixed) or inconstant (not fixed) rate, and also if it is a faster (steeper slope) or slower (more moderate slope) rate.

The following graph can demonstrate the aforementioned in the best way:

Rate of Change of a Function Represented Graphically

Let's observe the graph. We will notice that it is divided into 4 different branches. Now we will analyze each of the branches:

• Branch 1: the graph rises (increasing function) at a constant rate (straight line).
• Branch 2: The graph falls (decreasing function) at a constant rate (straight line).
• Branch 3: the graph rises (increasing function) at a constant rate (straight line) and more quickly than branch 1 (the slope is steeper).
• Branch 4: The graph falls (decreasing function) at a constant rate (straight line) and more slowly than branch 2 (the slope is more moderate).

Examples with solutions for Rate of change of a function represented graphically

Exercise #1

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.

Non-uniform

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.

Non-uniform

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.

Non-uniform

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.

Since the graph is a straight line - the rate of change is constant.

Uniform

Exercise #5

Given the following graph, determine whether function is constant

constant

Exercise #6

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

Uniform

Exercise #7

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

Non-uniform

Exercise #8

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

Non-uniform

Exercise #9

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

Non-uniform

Exercise #10

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

Uniform

Exercise #11

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

Uniform

Exercise #12

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

Uniform

Exercise #13

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

Uniform

Exercise #14

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

Non-uniform

Exercise #15

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