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Chapter 2: Problem 39

The statement \(f(4)=1\) corresponds to what ordered pair?

Short Answer

Expert verified
(4, 1)

Step by step solution

01

Identify the Function

The function given is represented as \(f(x)\). An ordered pair consists of two elements: an input (x-value) and an output (f(x)-value).
02

Recognize the Pair

In the statement \(f(4)=1\), the input (x-value) is 4 and the output (f(x)-value) is 1.
03

Form the Ordered Pair

Combine the input and the output to form the ordered pair, which is written as \((x, f(x))\). So, for the given statement, the ordered pair is \((4, 1)\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

function notation
Function notation is a standardized way to denote the relationship between inputs and outputs in mathematics. It is typically written as \(f(x)\) where \(f\) represents the function and \(x\) represents the input variable. The output, which is the result of applying the function to the input, is denoted as \(f(x)\). For example, if we have a function \(f\) and we input 4 into this function, and get 1 as the output, we write this as \(f(4)=1\). This notation tells us directly what the input and corresponding output are.
input-output relationship
Understanding the input-output relationship is crucial in working with functions. In the context of functions, the 'input' refers to the value that is fed into the function. It is often denoted as \(x\). The 'output' is the value that comes out of the function after applying the given rule to the input. It is usually written as \(f(x)\) where 'f' specifies the function and \(x\) the input. For example, in the statement \(f(4)=1\), 4 is the input and 1 is the output. This tells us that when we put 4 into the function \(f\), the result we obtain is 1.
coordinate pairs
Coordinate pairs are used to represent the input-output relationship in functions on a coordinate plane. These pairs are written as \((x, f(x))\) where \(x\) is the input and \(f(x)\) is the output. By plotting these coordinates, we can visualize the function. For instance, if given \(f(4)=1\), this translates to the ordered pair \( (4,1) \). Plotting \( (4,1) \) on a coordinate plane helps us see the point representing this input-output relationship, making it easier to understand how the function behaves.

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Most popular questions from this chapter

Evaluate the step function defined by \(f(x)=[x]\) for the given values of \(x\). $$ f(-9) $$

Evaluate the step function defined by \(f(x)=[x]\) for the given values of \(x\). $$ f(-0.09) $$

Graph the function. $$ m(x)=\left\\{\begin{array}{ll} 3 & \text { for }-4

Evaluate the function for the given values of \(x\). \(g(x)=\left\\{\begin{array}{ll}-2|x|-3 & \text { for } x \leq-2 \\ 5 x+6 & \text { for }-2

Graph the function. $$ r(x)=\left\\{\begin{array}{cl} x^{2}-4 & \text { for } x \leq 2 \\ 2 x-4 & \text { for } x>2 \end{array}\right. $$
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