# Variation of a Function - Examples, Exercises and Solutions

### Different Types of Rates of Change of a Function

The rate of change of a function describes the pace of modification that the variables $Y$ experience with respect to the change in the variables $X$.
The rate of change can be:

• $b>$ Constant Rate of Change - fixed
Describes a situation in which we will see constant intervals of variables $Y$ at constant intervals of variables $X$.
In a linear function (a straight line), the rate of change is constant and will be the slope of the function.
• Non-constant Rate of Change - not fixed
Describes a situation in which we will see different intervals of variables $Y$ at constant intervals of variables $X$.
In a function that is not linear (not a straight line), the rate of change will not be constant. Each part of the function will have a different slope.

We can see the rate of change represented in a graph, a table of values, or by creating steps or stairs in the graph of the function.

## Practice Variation of a Function

### Exercise #1

Given the following graph, determine whether function is constant

constant

### Exercise #2

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

Uniform

### Exercise #3

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

Non-uniform

### Exercise #4

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

Non-uniform

### Exercise #5

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

Non-uniform

### Exercise #1

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

Non-uniform

### Exercise #2

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

Non-uniform

### Exercise #3

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

Non-uniform

### Exercise #4

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

Uniform

### Exercise #5

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

Uniform

### Exercise #1

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

Uniform

### Exercise #2

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

Uniform

### Exercise #3

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

Uniform

### Exercise #4

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

Non-uniform

### Exercise #5

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