/*! 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 62 Refer to the function \(f=\\{(2,... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 62

Refer to the function \(f=\\{(2,3),(9,7),(3,4),(-1,6)\\} .\) Determine \(f(-1)\).

Short Answer

Expert verified
f(-1) = 6

Step by step solution

01

Identify the function pairs

Examine the function provided: offers the pairs \{(2,3), (9,7), (3,4), (-1,6)\}.The first element in each pair is the input (or \(x\)-value), and the second element is the output (or \(y\)-value).
02

Locate the input of interest

Identify which pair has the input \(-1\). Looking through the function pairs: (2,3), (9,7), (3,4), and (-1,6), find the pair containing the input value of \('-1'\).
03

Extract the corresponding output

In the pair \((-1, 6)\), the input value is \(-1\), and the corresponding output value is \(6\). Therefore, when \(f(-1)\) is evaluated, the output value is \(6\).

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.

functions in algebra
In algebra, functions play a vital role in describing the relationships between variables. A function is essentially a set of rules that assigns each input exactly one output. You can think of a function like a machine: you feed an input into the machine, and it produces an output based on the specific rule or equation defined.

For example, consider the function given in the exercise: \(f = \{(2,3),(9,7),(3,4),(-1,6)\}\). Here, the function is represented as a set of ordered pairs.

Each pair contains an input (the first element) and an output (the second element). By understanding this basic structure, you can learn to evaluate functions by finding outputs for given inputs.
input-output pairs
Input-output pairs are the building blocks of functions. They show how specific inputs connect to particular outputs.

In the provided function \(f = \{(2,3),(9,7),(3,4),(-1,6)\}\), each ordered pair represents an input-output relationship:
  • (2,3) means an input of 2 corresponds to an output of 3.
  • (9,7) means an input of 9 corresponds to an output of 7.
  • (3,4) means an input of 3 corresponds to an output of 4.
  • (-1,6) means an input of -1 corresponds to an output of 6.


Understanding these relationships helps in evaluating functions effectively. Each pair in the set gives clear information about what happens to a particular input when passed through the function.
determining function values
Determining function values involves identifying the output that corresponds to a given input. Let's break down the steps using the function from the exercise:

  • Step 1: Identify the function pairs. Given: \(f = \{(2,3),(9,7),(3,4),(-1,6)\}\). Take note of the pairs.

  • Step 2: Locate the input of interest. Look for the pair that has the input value \(-1\).

  • Step 3: Extract the corresponding output. Find which output value matches with the input \(-1\). Here, the corresponding pair is \((-1, 6)\).

  • Conclusion: So, the value of \(f(-1)\) is determined to be \(6\).


By following these steps systematically, you can determine the values of functions accurately.

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

Given \(h(x)=\frac{1}{x-6},\) evaluate \((h \circ h)(x)\) and write the domain in interval notation.

Refer to the functions \(r, p,\) and \(q .\) Evaluate the function and write the domain in interval notation. \(r(x)=-3 x \quad p(x)=x^{2}+3 x \quad q(x)=\sqrt{1-x}\) $$(r+q)(x)$$

Given \(g(x)=\sqrt{x-3}\), evaluate \((g \circ g)(x)\) and write the domain in interval notation.

a. Given \(m(x)=4 x^{2}+2 x-3,\) find \(m(-x)\). b. Find \(-m(x)\). c. Is \(m(-x)=m(x)\) ? d. Is \(m(-x)=-m(x)\) ? e. Is this function even, odd, or neither?

A bicycle wheel turns at a rate of 80 revolutions per minute (rpm). a. Write a function that represents the number of revolutions \(r(t)\) in \(t\) minutes. b. For each revolution of the wheels, the bicycle travels \(7.2 \mathrm{ft}\). Write a function that represents the distance traveled \(d(r)\) (in \(\mathrm{ft}\) ) for \(r\) revolutions of the wheel. c. Evaluate \((d \circ r)(t)\) and interpret the meaning in the context of this problem. d. Evaluate \((d \circ r)(30)\) and interpret the meaning in the context of this problem.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.