/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Determine whether or not the giv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 2

Determine whether or not the given table could possibly be a table of values of a function. Give reasons for your answer. $$\begin{array}{|l|c|c|c|c|c|} \hline \text { Input } & -5 & 3 & 0 & -3 & 5 \\ \hline \text { Output } & 0 & 3 & 0 & 5 & -3 \\ \hline \end{array}$$

Short Answer

Expert verified
Answer: Yes, the given table represents a function.

Step by step solution

01

Identify input and output values

From the given table, we can see that we have five input values, which are -5, 3, 0, -3, and 5. Corresponding to these input values, we have output values of 0, 3, 0, 5, and -3, respectively.
02

Check for unique outputs for each input

Now we need to verify whether each input value has exactly one output value or not. Input: -5, Output: 0 Input: 3, Output: 3 Input: 0, Output: 0 Input: -3, Output: 5 Input: 5, Output: -3 From the table, we can observe that each input value has a unique output value. No input has more than one output value.
03

Conclusion

Since each input value has exactly one output value, the given table represents a function.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Input-Output Table
An input-output table is a method used to represent relationships between inputs and their corresponding outputs in a structured way. These tables are extremely useful in identifying whether a set of data can represent a function. Each row within the table typically matches an input with its respective output, allowing for easy visualization of these pairings.

  • The left column consists of the inputs.
  • The right column consists of the outputs associated with each input.
The core purpose of an input-output table in the context of functions is to see if every input corresponds to exactly one output, which is a vital characteristic for classifying this relationship as a function.
Function Definition
Understanding the definition of a function is essential when analyzing an input-output table. At its core, a function is a specific type of relation between sets, where each element in the domain (all possible inputs) is related to exactly one element in the codomain (all possible outputs).

  • A function maps each input to one and only one output.
  • This unique relationship is what distinguishes functions from other types of relations.
In mathematical terms, if you have a function \(f(x)\), each input \(x\) will produce a single output \(f(x)\). This certainty is what defines the consistency and predictability of functions.
Unique Mapping
Unique mapping is a critical aspect of functions. It means every input in the relation must connect to a singular output鈥攏o exceptions. When evaluating an input-output table, check each input's corresponding output to verify this uniqueness.

  • Ensure no input pairs with multiple outputs.
  • If each input is paired with only one output, then the relation is likely a function.
For instance, in the provided exercise, each input such as -5, 3, 0, etc., has exactly one corresponding output value. This affirmation of unique mapping confirms that the data set meets the criteria of a function.
Precalculus
Precalculus serves as a bridge between basic algebra and the more advanced topics in calculus. It focuses on foundational concepts, including understanding functions, which are pivotal to mastering calculus.

  • One fundamental topic in precalculus is the study of functions, their representations, and behaviors.
  • Grasping unique input-output relationships prepares students for solving complex calculus problems.
Studying functions within precalculus not only helps in differentiating between valid functions and non-functions but also builds a strong mathematical foundation required for success in calculus, physics, engineering, and beyond.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the dimensions of a box with a square base that has a volume of 867 cubic inches and the smallest possible surface area, as follows. (a) Write an equation for the surface area \(S\) of the box in terms of \(x\) and \(h .[\) Be sure to include all four sides, the top, and the bottom of the box.] (b) Write an equation in \(x\) and \(h\) that expresses the fact that the volume of the box is 867 . (c) Write an equation that expresses \(S\) as a function of \(x\). [Hint: Solve the equation in part (b) for \(h\), and substitute the result in the equation of part (a).] (d) Graph the function in part (c), and find the value of \(x\) that produces the smallest possible value of \(S .\) What is \(h\) in this case?

List three different functions (other than the ones in Example 6 and Exercise 29 ), each of which is its own inverse. [Many correct answers are possible.]

Write the rule of a function g whose graph can be obtained from the graph of the function \(f\) by performing the transformations in the order given. \(f(x)=x^{2}+2 ;\) shift the graph horizontally 5 units to the left and then vertically upward 4 units.

The estimated number of 15 - to 24 -year-old people worldwide (in millions) who are living with HIV/AIDS in selected years is given in the table."$$\begin{array}{|l|c|c|c|c|c|} \hline \text { Year } & 2001 & 2003 & 2005 & 2007 & 2009 \\ \hline \begin{array}{l} \text { 15- to 24-year-olds } \\ \text { with HIV/AIDS } \end{array} & 12 & 14.5 & 17 & 19 & 20.5 \\ \hline \end{array}$$(a) Use linear regression to find a function that models this data, with \(x=0\) corresponding to 2000 (b) According to your function, what is the average rate of change in this HIV/AIDS population over any time period between 2001 and \(2009 ?\) (c) Use the data in the table to find the average rate of change in this HIV/AIDS population from 2001 to 2009 . How does this rate compare with the one given by the model? (d) If the model remains accurate, when will the number of people in this age group with HIV/AIDS reach 25 million?

It is possible to write every even natural number uniquely as the product of two natural numbers, one odd and one a power of two. For example: \(46=23 \times 2 \quad 36=9 \times 2^{2} \quad 8=1 \times 2^{3}\) Consider the function whose input is the set of even integers and whose output is the odd number you get in the above process. So if the input is \(36,\) the output is 9. If the input is \(46,\) the output is 23 (a) Write a table of values for inputs 2,4,6,8,10,12 and 14 (b) Find five different inputs that give an output of 3
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.