Understanding Ordered Pairs and Functions

Oct 13, 2025 by windailys.com 144 views

Understanding Ordered Pairs and Functions

In mathematics, an ordered pair is a pair of values in which the order of the values is important. It is often represented as (x, y), where x is the input value and y is the output value. A function, on the other hand, is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). In this article, we will focus on selecting ordered pairs of a given function.

The Given Function

The given function is $f(x) = 3 - 2x$ . This function takes an input value x and produces an output value y, which is calculated by subtracting 2 times x from 3.

Understanding the Task

The task is to select all the ordered pairs that are part of the given function. This means we need to find the values of x and y that satisfy the equation $f(x) = 3 - 2x$ .

Analyzing the Options

Let's analyze each option and determine if it is an ordered pair of the given function.

Option A: (0, 3)

To check if this is an ordered pair of the given function, we need to substitute x = 0 into the equation $f(x) = 3 - 2x$ .

$f(0) = 3 - 2(0)$ $f(0) = 3 - 0$ $f(0) = 3$

Since $f(0) = 3$ , this means that the ordered pair (0, 3) is indeed part of the given function.

Option B: (-2, -1)

To check if this is an ordered pair of the given function, we need to substitute x = -2 into the equation $f(x) = 3 - 2x$ .

$f(-2) = 3 - 2(-2)$ $f(-2) = 3 + 4$ $f(-2) = 7$

Since $f(-2) = 7$ , this means that the ordered pair (-2, -1) is not part of the given function.

Option C: (1, 0)

To check if this is an ordered pair of the given function, we need to substitute x = 1 into the equation $f(x) = 3 - 2x$ .

$f(1) = 3 - 2(1)$ $f(1) = 3 - 2$ $f(1) = 1$

Since $f(1) = 1$ , this means that the ordered pair (1, 0) is not part of the given function.

Option D: (-1, 5)

To check if this is an ordered pair of the given function, we need to substitute x = -1 into the equation $f(x) = 3 - 2x$ .

$f(-1) = 3 - 2(-1)$ $f(-1) = 3 + 2$ $f(-1) = 5$

Since $f(-1) = 5$ , this means that the ordered pair (-1, 5) is indeed part of the given function.

Option E: (2, -1)

To check if this is an ordered pair of the given function, we need to substitute x = 2 into the equation $f(x) = 3 - 2x$ .

$f(2) = 3 - 2(2)$ $f(2) = 3 - 4$ $f(2) = -1$

Since $f(2) = -1$ , this means that the ordered pair (2, -1) is indeed part of the given function.

Conclusion

In conclusion, the ordered pairs that are part of the given function are:

(0, 3)
(-1, 5)
(2, -1)

These ordered pairs satisfy the equation $f(x) = 3 - 2x$ , which means they are part of the given function.

Final Answer

The final answer is:

A. (0, 3)
D. (-1, 5)
E. (2, -1)
Q&A: Understanding Ordered Pairs and Functions =====================================================

Introduction

In our previous article, we discussed selecting ordered pairs of a given function. We analyzed each option and determined which ones were part of the function. In this article, we will answer some frequently asked questions about ordered pairs and functions.

Q: What is an ordered pair?

A: An ordered pair is a pair of values in which the order of the values is important. It is often represented as (x, y), where x is the input value and y is the output value.

Q: What is a function?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). In other words, a function takes an input value and produces an output value.

Q: How do I determine if an ordered pair is part of a function?

A: To determine if an ordered pair is part of a function, you need to substitute the input value (x) into the equation of the function and check if the output value (y) matches the given ordered pair.

Q: What is the difference between an ordered pair and a coordinate point?

A: An ordered pair is a pair of values in which the order of the values is important, whereas a coordinate point is a point on a coordinate plane. While an ordered pair can be used to represent a coordinate point, not all ordered pairs are coordinate points.

Q: Can an ordered pair have the same input value but different output values?

A: No, an ordered pair cannot have the same input value but different output values. By definition, an ordered pair is a pair of values in which the order of the values is important, so if the input value is the same, the output value must also be the same.

Q: Can a function have multiple ordered pairs with the same output value?

A: Yes, a function can have multiple ordered pairs with the same output value. This is because a function can take multiple input values and produce the same output value.

Q: How do I graph a function using ordered pairs?

A: To graph a function using ordered pairs, you need to plot the ordered pairs on a coordinate plane. Each ordered pair represents a point on the graph, and by connecting these points, you can visualize the graph of the function.

Q: What is the significance of ordered pairs in real-world applications?

A: Ordered pairs are used in many real-world applications, such as:

Calculating the cost of goods and services
Determining the coordinates of a location on a map
Analyzing data in statistics and data science
Modeling real-world phenomena in physics and engineering

Conclusion

In conclusion, ordered pairs and functions are fundamental concepts in mathematics that have many real-world applications. By understanding how to determine if an ordered pair is part of a function, you can apply this knowledge to a wide range of problems and situations.

Final Answer

The final answer is:

Q: What is an ordered pair? A: An ordered pair is a pair of values in which the order of the values is important.
Q: What is a function? A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
Q: How do I determine if an ordered pair is part of a function? A: To determine if an ordered pair is part of a function, you need to substitute the input value (x) into the equation of the function and check if the output value (y) matches the given ordered pair.