/*! 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} Q. 76 In Problems 75鈥�80, for the giv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 76 (page 157)

In Problems 75鈥�80, for the given functions f and g,

(a) Graph fand gon the same Cartesian plane.

(b) Solvefx=gx.

(c) Use the result of part (b) to label the points of intersection of the graphs of fand g.

(d) Shade the region for which fx>gx.that is, the region below f and aboveg.

fx=-2x-1;gx=x2-9.

Short Answer

Expert verified

(a) The graph of fand gis

(b) The value ofx=-2,4.

(c) The point of intersection is2,-5,-4,7.

(d) The shaded region is

Step by step solution

01

Part (a) Step 1. Given information

It is given thatfx=-2x-1;gx=x2-9.We need to graphfandgon the same cartesian plane.

02

Step 2. Graph fx and gx

03

Part (b) Step 1. Given information

It is given thatfx=-2x-1;gx=x2-9.We need to solvefx=gx.

04

Step 2. Simplify

fx=gx.

-2x-1=x2-9.

x2+2x-8=0.

x=-2卤22-4路1-82路1.

=-2卤4+322路1.

=-2卤362.

=-2卤62.

role="math" localid="1647274107418" x=-2+62=2,andx=-2-62=-4.

The value of the function fand gare equal when x=2,-4.

05

Part (c) Step 1. Given information

It is given that fx=-2x-1;gx=x2-9.We need to use the result of part (b) to label the point of intersection.

06

Step 2. Simplify

Let y=-2x-1.

y=gx=x2-9.

Whenx=2,y=-22-1=-5.

When x=-4,y=-2路-4-1=7.

The point of intersection is2,-5,-4,7.

07

Part (d) Step 1. Given information

It is given thatfx=-2x-1;gx=x2-9.We need to label the shaded region for whichfx>gx.

08

Step 2. Shaded the region

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

Solve:60x-900=-15x+2850.

Match each graph to one the following functions.

f(x)=x2-2x+1

In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

If h(x)=-3x+4,then

a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.

What is the domain of the functionx2-16?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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.