/*! 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 10 Graph the given functions. $$y... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 10

Graph the given functions. $$y=-3$$

Short Answer

Expert verified
The graph is a horizontal line at y = -3.

Step by step solution

01

Understanding the Equation

The equation given is a horizontal line, as there is no variable 'x' present. This means that for any value of 'x', 'y' remains constant at -3.
02

Identify the Graph Type

Since 'y' remains constant, the graph is a horizontal line. This indicates that the graph runs parallel to the x-axis, intercepting the y-axis at -3.
03

Plotting Key Points

To graph the equation, first locate the point on the y-axis at y = -3. This point is (0, -3).
04

Drawing the Line

Draw a horizontal line through the point (0, -3). Extend this line to both the positive and negative directions of the x-axis. The line should stretch towards infinity on either side at the same y-level, -3.

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.

Horizontal Line
In mathematics, understanding what a horizontal line is can simplify the graphing process significantly. A horizontal line is characterized by having a constant y-value, meaning it does not rise or fall as it moves along the x-axis. This type of line is parallel to the x-axis, remaining flat and unchanging regardless of the x-coordinate.
It is important to highlight that in equations like \(y = -3\), the absence of the "x" variable signifies the equation remains constant for all values of "x." Essentially, no matter what x-value you select, y will always equal -3, creating a straight line that stretches infinitely in the horizontal direction.
Graph Interpretation
Graph interpretation involves reading and understanding what a graph depicts about a relationship, often between two variables like x and y. To interpret a graph of a horizontal line like \(y = -3\), start by observing that the line is flat and extends left to right. This signifies that the y-value, -3, remains constant across all x-values.
Recognizing this can help you make predictions and observations:
  • The horizontal line does not move up or down, reinforcing the unchanging y-value.
  • Any point on this line will have a y-coordinate of -3, showing that x-values have no effect.
  • Such graphs can suggest situations where an output is invariant despite changes in input.
In real-world contexts, this could describe phenomena like a fixed price rate or a static temperature over time.
Coordinate System
The coordinate system serves as a framework for graphing equations like \(y = -3\). Understanding it is crucial for plotting points and interpreting graphs. A coordinate plane is composed of two perpendicular number lines that intersect at their zero points, called the origin (0,0). These number lines are the x-axis (horizontal) and the y-axis (vertical).
On this plane, any point can be described with an ordered pair \((x, y)\). For horizontal lines:
  • The x-axis helps determine how far left or right a point is from the origin.
  • Meanwhile, the y-value remains constant, indicating its height on the vertical y-axis is unchanged.
Thus, in the equation \(y = -3\), every point along this line will have different x-coordinates but will all maintain a y-coordinate of -3, perfectly illustrating the utility of the coordinate system in graphing.
Plotting Points
Plotting points is a foundational skill in graphing that involves marking specific locations on the coordinate plane. When graphing a simple horizontal line, such as \(y = -3\), the process involves just a few straightforward steps. First, identify a point where y is -3.
Begin by locating the y-value of -3 on the y-axis. From there, any chosen x-value will result in a coordinate \((x, -3)\). Some potential points to plot include \((0, -3)\), \((1, -3)\), and \((-2, -3)\).
  • These points are then marked on the graph, keeping them horizontally aligned because their vertical position doesn't change.
  • Once these points are plotted, draw a line connecting them, remembering it should continue infinitely along the x-axis.
This simple technique transforms the abstraction of an equation into a concrete visual representation, making understanding and analysis much simpler.

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

Solve the given problems. A person considering the purchase of a car has two options: (1) purchase it for \(\$ 35,000,\) or (2) lease it for three years for payments of \(\$ 450 /\) month plus \(\$ 2000\) down, with the option of buying the car at the end of the lease for \(\$ 18,000\). (a) For the lease option, express the amount \(P\) paid as a function of the numbers of months \(m\). (b) What is the difference in the total cost if the person keeps the car for the three years, and then decides to buy it?

Graph the given functions. $$y=x^{2}-3 x+1$$

Graph the indicated functions. An airline requires that any carry-on bag has total dimensions (length \(+\) width \(+\) height) that do not exceed 45 in. For a carryon that just meets this requirement and \(h\) as a length that is twice the width, express the volume \(V\) as a function of the width \(w\). Draw the graph of \(V=f(w)\)

A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator. \(y=-4 x,\) up \(4,\) right 3

Graph the indicated functions. A land developer is considering several options of dividing a large tract into rectangular building lots, many of which would have perimeters of \(200 \mathrm{m}\). For these, the minimum width would be \(30 \mathrm{m}\) and the maximum width would be \(70 \mathrm{m}\). Express the areas \(A\) of these lots as a function of their widths \(w\) and plot the graph.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.