# Variation of a Function - Examples, Exercises and Solutions

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

## Examples with solutions for Variation of a Function

### 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.
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