Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q 3. (page 915)

Let f : R → R be a function of a single variable. Explain why the graph of f is a subset of R2.

Short Answer

Expert verified

The graph of f is a subset of as the graph is plotted using two axes: x-axis and y-axis

Step by step solution

01

Step 1. Given information

Function isf:R→R

02

Step 2. Explanation

A graph is a graphical portrayal represents the relationship between the dependent and independent variables.

The input and output values are used to display the curve of a function.

For the function y=f(x), graph is to be mapped between two variables, 'x' and 'y'.

As a result, the graph will be plotted with two axes.

The concept of R2is as follows.

As a result, f graph must be a subset ofR2

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Describe the meanings of each of the following mathematical expressions :

fyx0,y0

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x,y)=xy′P=(4,3)

Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.

f(x,y)=x+yx2+y2,P=(1,2),v=⟨3,−2⟩

Letz=(f(x,y))n.Showthat∂z∂x=n(f(x,y))n-1∂f∂xand∂z∂y=n(f(x,y))n-1∂f∂y.

In Exercises 37-42, use the partial derivatives of role="math" localid="1650186824938" fx,y=xyand the point e,3specified to

afind the equation of the line tangent to the surface defined by the function in the xdirection,

bfind the equation of the line tangent to the surface defined by the function in the ydirection, and

cfind the equation of the plane containing the lines you found in parts aand b.

See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Decision Maths

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.

Sign-up for free