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Chapter 3: Q. 5 (page 171)

In problems 3-6, use the figure to solve each inequality.

a) g(x)鈮�f(x)

b)f(x)>g(x)

Short Answer

Expert verified

(a)[-2,1]

(b) (-鈭�,-2)or(1,鈭�)

Step by step solution

01

Part (a) Step 1. Given Information  

It is given that g(x)鈮�f(x)and the graph is,

02

Part (a) Step 2. Observe the graph  

  • From the graph, it is observed that the value of g(x)is greater than or equal to f(x)for localid="1646313863885" role="math" -2鈮�x鈮�1.
  • In the set builder form, for g(x)鈮�f(x), localid="1646313876888" role="math" {x|-2鈮�x鈮�1}. Also, in interval notation it is denoted as [-2,1].
03

Part (b) Step 1. Given Information   

It is given that, f(x)>g(x)and the graph is,

04

Part (b) Step 2. Observe the graph   

  • From the graph, it is observed that the value of f(x)is greater than g(x)for x<-2orx>1.
  • In the set builder form, forf(x)>g(x),{x|x<-2orx>1}. Also, in interval notation it is denoted as role="math" localid="1646313809222" (-鈭�,-2)or(1,鈭�).

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Most popular questions from this chapter

In Problems 7鈥�22, solve each inequality.

4x2+9<6x

On one set of coordinate axes, graph the family of parabolas f(x)=x2+2x+cfor c = -3, c = 0, and c = 1. Describe the characteristics of a member of this family.

In Problems 6鈥� 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).

fx=2x+12+4

In Problems 21鈥�28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

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If p(x)=-x+6,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.
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