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,...
Related questions
Question
![**Linear Functions and Graphing**
Consider the function values given below:
\[ f\left(\frac{3}{5}\right) = \frac{1}{2} \quad \text{and} \quad f(2) = 4 \]
**(a) Write the linear function \( f \) that has the given function values.**
\[ f(x) = \frac{21}{10}x - \frac{1}{15} \]
**(b) Sketch the graph of the function.**
The graph displayed is a Cartesian coordinate system where the function \( f(x) = \frac{21}{10}x - \frac{1}{15} \) is plotted. The vertical axis represents the \( y \)-values, and the horizontal axis represents the \( x \)-values. The grid is marked with integers ranging from -10 to 10 on both the \( x \)-axis and the \( y \)-axis. The line passes through the given function values, reflecting a linear relationship with a slope of \( \frac{21}{10} \) and a \( y \)-intercept at \( -\frac{1}{15} \).
***
In this example, you can see how to interpret function values and correctly graph a linear function using the given data points. Understanding these basics is crucial for working with linear equations and functions in algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86020f22-4efe-437b-8b05-308770976ff7%2F36ed6282-c781-49ef-8b3c-502cfb5f848d%2Fkxuizm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Linear Functions and Graphing**
Consider the function values given below:
\[ f\left(\frac{3}{5}\right) = \frac{1}{2} \quad \text{and} \quad f(2) = 4 \]
**(a) Write the linear function \( f \) that has the given function values.**
\[ f(x) = \frac{21}{10}x - \frac{1}{15} \]
**(b) Sketch the graph of the function.**
The graph displayed is a Cartesian coordinate system where the function \( f(x) = \frac{21}{10}x - \frac{1}{15} \) is plotted. The vertical axis represents the \( y \)-values, and the horizontal axis represents the \( x \)-values. The grid is marked with integers ranging from -10 to 10 on both the \( x \)-axis and the \( y \)-axis. The line passes through the given function values, reflecting a linear relationship with a slope of \( \frac{21}{10} \) and a \( y \)-intercept at \( -\frac{1}{15} \).
***
In this example, you can see how to interpret function values and correctly graph a linear function using the given data points. Understanding these basics is crucial for working with linear equations and functions in algebra.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education