/*! 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 57 Graph each linear or constant fu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 57

Graph each linear or constant function. Give the domain and range. \(f(x)=x\)

Short Answer

Expert verified
The domain and range of f(x)=x are both all real numbers. Graph a straight line through points like (-2,-2), (0,0), and (2,2).

Step by step solution

01

Identify the Function Type

Observe that the given function is a linear function in the form of f(x)=x,
02

Find Several Points on the Graph

Choose several values for x and find the corresponding y values (f(x)). For example, if x=-2, then f(x)=-2; if x=0, then f(x)=0; if x=2, then f(x)=2.
03

Plot the Points

Draw the points found in the previous step on a coordinate plane: (-2, -2), (0, 0), and (2, 2).
04

Draw the Line

Connect the points with a straight line. This is the graph of the linear function f(x)=x.
05

Determine the Domain

Since it is a linear function, the domain is all real numbers. This means x can be any real number.
06

Determine the Range

The range of the function is also all real numbers. This means f(x) can take any real number value.

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.

Domain and Range
When dealing with functions, it's important to understand the concepts of domain and range. These terms help define which values we can use and obtain from a function.

The domain refers to all the possible input values (x-values) that you can plug into the function. For a linear function like f(x)=x, the domain is all real numbers because you can input any real number into the function.

The range is all the possible output values (y-values) the function can produce. In our example, f(x) = x, the output value is the same as the input value, making the range also all real numbers. Basically, any y-value you can think of will find an x-value that outputs it.
Coordinate Plane
Graphs of functions are plotted on a coordinate plane.

The coordinate plane is a two-dimensional surface where we can represent mathematical relationships. It consists of two perpendicular lines, or axes: the horizontal axis (x-axis) and the vertical axis (y-axis).
  • The point where the axes intersect is called the origin, denoted as (0, 0).
  • Each point on the plane is identified by an ordered pair (x, y), where 'x' denotes the horizontal position, and 'y' denotes the vertical position.


For our linear function f(x)=x, we chose points such as (-2, -2), (0, 0), and (2, 2). Each of these points is plotted on the coordinate plane. Once these points are plotted, you can connect them with a straight line to visualize the function.
Linear Function
A linear function is a function that graphs to a straight line. Linear functions have the general form f(x)=mx+b, where 'm' is the slope and 'b' is the y-intercept.

In our case, the function is f(x)=x. Here, the slope 'm' is 1, and the y-intercept 'b' is 0. This means the line goes through the origin (0, 0) and rises at a 45-degree angle.
  • To graph a linear function, start by finding several points (x, y) that satisfy the equation.
  • Plot these points on the coordinate plane.
  • Draw a straight line that passes through all the points.


Understanding linear functions helps in many areas of math and science as they model relationships where there's a constant rate of change.

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

For each pair of functions, find \((f g)(x) .\) $$ f(x)=x+1, \quad g(x)=2 x-3 $$

The cost in dollars to produce \(x\) youth baseball caps is \(C(x)=4.3 x+75 .\) The revenue in dollars from sales of \(x\) caps is \(R(x)=25 x\) (a) Write and simplify a function \(P\) that gives profit in terms of \(x\). (b) Find the profit if 50 caps are produced and sold.

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following. $$ \left(\frac{h}{g}\right)\left(-\frac{3}{2}\right) $$

Determine whether each relation defines y as a function of \(x .\) (Solve for y first if necessary.) Give the domain. $$ x=y^{6} $$

Let \(f(x)=x^{2}-9, g(x)=2 x,\) and \(h(x)=x-3 .\) Find each of the following $$ (f g)(0) $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.