/*! 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 19 Graph each line. Give the domain... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 19

Graph each line. Give the domain and range. $$x=3$$

Short Answer

Expert verified
Domain: {3}; Range: (-鈭�, 鈭�)

Step by step solution

01

Understand the Equation

The equation given is a vertical line. For any vertical line, the equation is in the form of \( x = a \) where \( a \) is a constant.
02

Plot the Line on a Graph

To plot the line \( x = 3 \), find the point on the x-axis where \( x = 3 \). From this point, draw a straight vertical line.
03

Determine the Domain

The domain of a vertical line \( x = 3 \) includes only one value: \( x = 3 \). Hence, the domain is \[ \{3\} \].
04

Determine the Range

The range of a vertical line is all possible values of \( y \). Since the line extends infinitely up and down, the range is \[ (-\infty, \infty) \].

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.

vertical line equation
A vertical line has a unique property: it runs straight up and down. This means it does not slant or angle but is perfectly perpendicular to the x-axis. The equation for any vertical line is in the form of \( x = a \), where \( a \) is a constant value. This equation tells us that no matter what point you choose on the line, the x-coordinate will always be \( a \). For example, in the exercise \( x = 3 \), this means every point on the line will have an x-coordinate of 3. Understanding this is key to recognizing and plotting vertical lines on a graph.
domain of vertical line
The domain of a function is all the possible values that x can take. For a vertical line like \( x = 3 \), x is always 3. This means the line is fixed in place at \( x = 3 \) and does not extend horizontally. As a result, the domain is very limited and consists of only one value: \( x = 3 \). Therefore, we can write the domain as \({3}\). This limitation is a unique characteristic of vertical lines and distinguishes them from other types of lines which usually have a broader domain.
range of vertical line
While the domain of a vertical line is constrained, its range is quite the opposite. The range of a function includes all possible values that y can take. For a vertical line like \( x = 3 \), there are no restrictions on the values of y. The line extends infinitely upwards and downwards, which means that it covers all possible y-values. Therefore, the range of a vertical line is \((-\infty, \infty)\). This means the line reaches in both positive and negative directions along the y-axis without any bounds.

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

Graph each linear function. Identify any constant functions. Give the domain and range. $$f(x)=-2 x$$

Plot each point, and then plot the points that are symmetric to the given point with respect to the ( \(a\) ) \(x\) -axis, (b) y-axis, and (c) origin. $$(-4,-2)$$

(a) find the center-radius form of the equation of each circle, and (b) graph it. center \((5,-4),\) radius 7

Find the function \(g(x)=a x+b\) whose graph can be obtained by translating the graph of \(f(x)=2 x+5\) up 2 units and to the left 3 units.

An equation that defines \(y\) as a function of \(x\) is given. (a) Solve for \(y\) in terms of \(x\) and $$\text {replace \(y\) with the function notation } f(x) . \text { (b) Find } f(3)$$. $$y-3 x^{2}=2+x$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

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.