/*! 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 68 Begin by graphing the square roo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 68

Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$g(x)=\sqrt{x}+1$$

Short Answer

Expert verified
The graph of \(g(x)=\sqrt{x}+1\) is a half parabola beginning at the point (0,1) and expanding towards the positive x-axis. It is similar to the base function \(f(x)=\sqrt{x}\), but is shifted upward by one unit.

Step by step solution

01

Graph the Base Function \(f(x)=\sqrt{x}\)

Start by plotting the square root function. This function forms a half parabola that begins at the origin (0,0) and expands towards the right or positive x-axis. Prevalent points on this graph are (0,0), (1,1), (4,2), and (9,3). The shape of the graph is determined by the fact that the square root of x increases as x increases, but it does so at a decelerating rate. Add these points to the graph and connect them smoothly for the visual illustration of \(f(x)=\sqrt{x}\)
02

Understand the Transformation

Next, look at the transformation that turns \(f(x)\) into \(g(x)\). Given that \(g(x)=\sqrt{x}+1\), this represents a vertical shifting of the original function \(f(x)\) upwards by one unit. This means the entire graph of \(f(x)\) will be shifted up by a single unit. This is a simple transformation that does not alter the overall shape of the graph
03

Graph the Transformed Function \(g(x) = \sqrt{x}+1\)

To graph \(g(x)=\sqrt{x}+1\), move every point on the original graph (the graph of \(f(x)=\sqrt{x}\)) up by one unit. This results in the points (0,1), (1,2), (4,3), and (9,4). Plot these points and connect them smoothly to get the graph of \(g(x)=\sqrt{x}+1\). This, like \(f(x)\), will be a half parabola. However, it will start at (0,1) instead of the origin and expands towards the positive x-axis from there.

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

In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ (x+4)^{2}+(y+5)^{2}=36 $$

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ (x+2)^{2}+y^{2}=16 $$

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}-6 y-7=0 $$

What does it mean if a function \(f\) is increasing on an interval?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.