Finding the Set of Ordered Pairs

Oct 13, 2025 by talynt.org 91 views

Introduction

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. The function is often denoted as h(x), where x is the input and h(x) is the output. In this article, we will explore the function h(x) = -x + 2 and describe the set of ordered pairs that satisfy this function.

The Function h(x) = -x + 2

The function h(x) = -x + 2 is a linear function, which means that it has a constant rate of change. The graph of this function is a straight line with a negative slope. To understand the set of ordered pairs for this function, we need to find the values of x and h(x) that satisfy the equation h(x) = -x + 2.

Finding the Set of Ordered Pairs

To find the set of ordered pairs, we need to find the values of x that satisfy the equation h(x) = -x + 2. We can do this by substituting different values of x into the equation and solving for h(x).

For example, if we substitute x = 2 into the equation, we get:

h(2) = -(2) + 2 h(2) = 0

So, the ordered pair (2, 0) satisfies the equation h(x) = -x + 2.

If we substitute x = 3 into the equation, we get:

h(3) = -(3) + 2 h(3) = -1

So, the ordered pair (3, -1) satisfies the equation h(x) = -x + 2.

We can continue this process by substituting different values of x into the equation and solving for h(x). However, we need to be careful and make sure that the values of x are greater than or equal to 2, as specified in the problem.

The Set of Ordered Pairs

After finding the values of x and h(x) that satisfy the equation h(x) = -x + 2, we can write the set of ordered pairs as:

{(x, h(x)) | h(x) = -x + 2; x ≥ 2}

This set of ordered pairs represents the function h(x) = -x + 2 and includes all the points that satisfy the equation.

Graphing the Function

To visualize the function h(x) = -x + 2, we can graph the set of ordered pairs. The graph will be a straight line with a negative slope, as expected for a linear function.

Properties of the Function

The function h(x) = -x + 2 has several properties that are worth noting:

Domain: The domain of the function is all real numbers x ≥ 2.
Range: The range of the function is all real numbers h(x) ≤ 2.
Slope: The slope of the function is -1, which means that the function has a constant rate of change.
Y-intercept: The y-intercept of the function is 2, which means that the function passes through the point (0, 2).

Conclusion

Introduction

In our previous article, we explored the function h(x) = -x + 2 and described the set of ordered pairs that satisfy this function. In this article, we will answer some frequently asked questions about the function h(x) = -x + 2.

Q: What is the domain of the function h(x) = -x + 2?

A: The domain of the function h(x) = -x + 2 is all real numbers x ≥ 2. This means that the function is defined for all values of x that are greater than or equal to 2.

Q: What is the range of the function h(x) = -x + 2?

A: The range of the function h(x) = -x + 2 is all real numbers h(x) ≤ 2. This means that the function can take on any value that is less than or equal to 2.

Q: What is the slope of the function h(x) = -x + 2?

A: The slope of the function h(x) = -x + 2 is -1. This means that the function has a constant rate of change, and for every unit increase in x, the value of h(x) decreases by 1 unit.

Q: What is the y-intercept of the function h(x) = -x + 2?

A: The y-intercept of the function h(x) = -x + 2 is 2. This means that the function passes through the point (0, 2), and when x is equal to 0, the value of h(x) is equal to 2.

Q: How do I graph the function h(x) = -x + 2?

A: To graph the function h(x) = -x + 2, you can use a graphing calculator or a computer program. Alternatively, you can plot the points that satisfy the equation h(x) = -x + 2 and draw a straight line through them.

Q: Can I use the function h(x) = -x + 2 to model real-world situations?

A: Yes, the function h(x) = -x + 2 can be used to model real-world situations where there is a linear relationship between two variables. For example, you could use this function to model the cost of producing a certain number of items, where the cost decreases by a fixed amount for each additional item produced.

Q: How do I find the value of h(x) for a given value of x?

A: To find the value of h(x) for a given value of x, you can substitute the value of x into the equation h(x) = -x + 2 and solve for h(x). For example, if you want to find the value of h(4), you would substitute x = 4 into the equation and get h(4) = -(4) + 2 = -2.

Q: Can I use the function h(x) = -x + 2 to solve equations?

A: Yes, the function h(x) = -x + 2 can be used to solve equations where the variable is x. For example, if you have the equation h(x) = 1, you can substitute h(x) = -x + 2 into the equation and solve for x.

Conclusion

In this article, we answered some frequently asked questions about the function h(x) = -x + 2. We hope that this article has been helpful in understanding the function and its properties. If you have any further questions, please don't hesitate to ask.