/*! 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 113 What is the graph of a function?... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 113

What is the graph of a function?

Short Answer

Expert verified
The graph of a function is a visual depiction of the relationship between inputs (x-values) and their corresponding outputs (y-values), represented as points on a coordinate plane. Each point on the graph comprises an ordered pair \((x, f(x))\), which reflects the output \(f(x)\) yielded for each input \(x\) by the function.

Step by step solution

01

Define 'Function'

First, let's define what a function is. A function is a rule that assigns each input exactly one output. In mathematical terms, if \(x\) is the input and \(y\) is the output, then this relationship can be denoted as: \(y=f(x)\).
02

Explain 'Graph of a Function'

The graph of a function is a visual representation or a diagram that shows this input-output relationship that a function establishes. This graphical representation is usually drawn on a plane with two axes: x-axis (horizontal) and y-axis (vertical). Each point on the graph represents an ordered pair \((x, f(x))\), which means for every input \(x\), its corresponding output \(f(x)\) is plotted as a point on the graph.
03

Example of Graph of a Function

For example, consider a simple function \(f(x) = x^2\). The graph of this function will start at point (0,0) since \(0^2 = 0\), then curve upwards as the square of x is positive for all real numbers. So, every point on this curve will have the x-coordinate as an input and y-coordinate as the output of the function.

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!

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25\) and \((x-2)^{2}+(y+3)^{2}=36\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this point of contact. Write an equation in point-slope form for the line tangent to the circle whose equation is \(x^{2}+y^{2}=25\) at the point \((3,-4)\)

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=(2 x-5)^{3}$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-10 x-6 y-30=0$$

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned} (x-2)^{2}+(y+3)^{2} &=4 \\ y &=x-3 \end{aligned}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.