Question

# How can you determine whether a relation is a function ?

Hint:

### A relation is a set of ordered pairs. The set of the first components of each ordered pair is called the domain and the set of the second components of each ordered pair is called the range.

## The correct answer is: independent variable.

### Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.

{(1, 2),(2, 4),(3, 6),(4, 8),(5, 10)}

The domain is {1,2,3,4,5}. The range is {2,4,6,8,10}.

Note that each value in the domain is also known as an input value, or independent variable. Each value in the range is also known as an output value, or dependent variable.

A function, f, is a relation that assigns a single value in the range to each value in the domain*.* In other words, no *x*-values are repeated.

For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, {1,2,3,4,5}, is paired with exactly one element in the range, {2,4,6,8,10}.

Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as

{(odd, 1),(even, 2),(odd, 3),(even, 4),(odd, 5)}

Notice that each element in the domain, {even, odd} is *not* paired with exactly one element in the range, {1,2,3,4,5}. For example, the term “odd” corresponds to three values from the domain, {1,3,5} and the term “even” corresponds to two values from the range, {2,4}. This violates the definition of a function, so this relation is not a function.

Each value in the domain is also known as an input value, or independent variable. Each value in the range is also known as an output value, or dependent variable.

### Related Questions to study

### Melody starts at her house and rides her bike for 10 minutes to a friend’s house. She stays at her friend’s house for 60 minutes. Sketch a graph that represents this description.

### Melody starts at her house and rides her bike for 10 minutes to a friend’s house. She stays at her friend’s house for 60 minutes. Sketch a graph that represents this description.

### Is the following relation forms a function ? Explain.

(49,13)(61,36)(10,27)(76,52)(23,52)

**Note:** All functions are relations but all relations are not functions.

### Is the following relation forms a function ? Explain.

(49,13)(61,36)(10,27)(76,52)(23,52)

**Note:** All functions are relations but all relations are not functions.

### Anu’s Mother drives to the gas station and fills up her tank. Then she drives to the market. Sketch the graph that shows the relationship between the amount of fuel in the gas tank of her car and time

### Anu’s Mother drives to the gas station and fills up her tank. Then she drives to the market. Sketch the graph that shows the relationship between the amount of fuel in the gas tank of her car and time

### When a new laptop became available in a store, the number sold in the first week was high. Sales decreased over the next two weeks and then they remained steady over the next two weeks. The following week, the total number sold by the store increased slightly. Sketch the graph that represents this function over the six weeks.

.

### When a new laptop became available in a store, the number sold in the first week was high. Sales decreased over the next two weeks and then they remained steady over the next two weeks. The following week, the total number sold by the store increased slightly. Sketch the graph that represents this function over the six weeks.

.

### Which of the given statements is NOT a result of Reflexive property?

### Which of the given statements is NOT a result of Reflexive property?

### Taylor has tracked the number of students in his grade since third grade. He records his data in the table below. Is the relation a function ? Explain.

**Note**: All functions are relations but all relations are not functions.

### Taylor has tracked the number of students in his grade since third grade. He records his data in the table below. Is the relation a function ? Explain.

**Note**: All functions are relations but all relations are not functions.

### What relationship between money (in$) and time (in M) does this graph show. Write a description of the given graph

### What relationship between money (in$) and time (in M) does this graph show. Write a description of the given graph

### Find the GCF (GCD) of terms of the given polynomial.

### Find the GCF (GCD) of terms of the given polynomial.

### An airplane takes 15 minutes to reach its cruising altitude. The plane cruises at that altitude for 90 minutes , and then descend for 20 min before it lands. Sketch the graph of the height of the plane over the time

### An airplane takes 15 minutes to reach its cruising altitude. The plane cruises at that altitude for 90 minutes , and then descend for 20 min before it lands. Sketch the graph of the height of the plane over the time

### Is the relation shown in the table a function ? Explain

All functions are relations but all relations are not functions.

### Is the relation shown in the table a function ? Explain

All functions are relations but all relations are not functions.

### Is the relation shown in the table a function ? Explain

All functions are relations but all relations are not functions.

### Is the relation shown in the table a function ? Explain

All functions are relations but all relations are not functions.

### Solve 0.14x + 0.12 = 0.35x − 2.4. Write a reason for each step.

### Solve 0.14x + 0.12 = 0.35x − 2.4. Write a reason for each step.

### Does the relation below shows represent a function ? Explain.

(-2,2)(-7,1) (-3,9)(3,4)(-9,5)(- 6,8)

**Note:** All functions are relations but all relations are not functions.

### Does the relation below shows represent a function ? Explain.

(-2,2)(-7,1) (-3,9)(3,4)(-9,5)(- 6,8)

**Note:** All functions are relations but all relations are not functions.

### The set of ordered pairs (1,19)(2,23) (3,23) (4,29)(5,31) represents the number of tickets sold to a fundraiser. The input values represents the day and the output values represents the number of tickets sold on that day.

a) Make an arrow diagram that represents the relation

b) Is the relation a function ? Explain.

**Note:** All functions are relations but all relations are not functions.

### The set of ordered pairs (1,19)(2,23) (3,23) (4,29)(5,31) represents the number of tickets sold to a fundraiser. The input values represents the day and the output values represents the number of tickets sold on that day.

a) Make an arrow diagram that represents the relation

b) Is the relation a function ? Explain.

**Note:** All functions are relations but all relations are not functions.