Homework Help is Here – Start Your Trial Now!
Math
Algebra
For the equation y =x - 2, (a) create a table with ordered pairs that are solutions of the equation, and (b) graph the equation. (a) Complete the following table of ordered pairs that are solutions of the equation. y - 1 1 2

For the equation y =x - 2, (a) create a table with ordered pairs that are solutions of the equation, and (b) graph the equation. (a) Complete the following table of ordered pairs that are solutions of the equation. y - 1 1 2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
### Solving and Graphing the Equation \( y = x^3 - 2 \) For the given equation \( y = x^3 - 2 \): 1. **Create a table with ordered pairs that are solutions of the equation:** #### Step (a): Fill in the ordered pairs. Use the given values of \( x \) to calculate the corresponding values of \( y \). | \( x \) | \( y \) | |--------|--------| | -1 | | | 0 | | | 1 | | | 2 | | **Calculations:** - For \( x = -1 \): \( y = (-1)^3 - 2 = -1 - 2 = -3 \) - For \( x = 0 \): \( y = 0^3 - 2 = 0 - 2 = -2 \) - For \( x = 1 \): \( y = 1^3 - 2 = 1 - 2 = -1 \) - For \( x = 2 \): \( y = 2^3 - 2 = 8 - 2 = 6 \) Here is the completed table: | \( x \) | \( y \) | |--------|--------| | -1 | -3 | | 0 | -2 | | 1 | -1 | | 2 | 6 | 2. **Graph the equation based on these ordered pairs.** To graph this equation, plot each of the ordered pairs \((-1, -3)\), \((0, -2)\), \((1, -1)\), and \((2, 6)\) on a coordinate plane. Draw a smooth curve that passes through these points to represent the equation \( y = x^3 - 2 \). ### Explanation of the Graph: - The graph of \( y = x^3 - 2 \) is a cubic curve. - It is symmetrical about the origin. - It crosses the y-axis at \( (0, -2) \). This activity helps visualize the correspondence between the values of x and y for the provided equation.
Transcribed Image Text:### Solving and Graphing the Equation \( y = x^3 - 2 \) For the given equation \( y = x^3 - 2 \): 1. **Create a table with ordered pairs that are solutions of the equation:** #### Step (a): Fill in the ordered pairs. Use the given values of \( x \) to calculate the corresponding values of \( y \). | \( x \) | \( y \) | |--------|--------| | -1 | | | 0 | | | 1 | | | 2 | | **Calculations:** - For \( x = -1 \): \( y = (-1)^3 - 2 = -1 - 2 = -3 \) - For \( x = 0 \): \( y = 0^3 - 2 = 0 - 2 = -2 \) - For \( x = 1 \): \( y = 1^3 - 2 = 1 - 2 = -1 \) - For \( x = 2 \): \( y = 2^3 - 2 = 8 - 2 = 6 \) Here is the completed table: | \( x \) | \( y \) | |--------|--------| | -1 | -3 | | 0 | -2 | | 1 | -1 | | 2 | 6 | 2. **Graph the equation based on these ordered pairs.** To graph this equation, plot each of the ordered pairs \((-1, -3)\), \((0, -2)\), \((1, -1)\), and \((2, 6)\) on a coordinate plane. Draw a smooth curve that passes through these points to represent the equation \( y = x^3 - 2 \). ### Explanation of the Graph: - The graph of \( y = x^3 - 2 \) is a cubic curve. - It is symmetrical about the origin. - It crosses the y-axis at \( (0, -2) \). This activity helps visualize the correspondence between the values of x and y for the provided equation.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS