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Chapter 2: Q. 7 (page 68)

If the domain of fis all real numbers in the interval [0,7]and the domain of g is all real numbers in the interval [-2,5], the domain of f+gis all real numbers in the interval _________.

Short Answer

Expert verified

If the domain of fis all real numbers in the interval[0,7]and the domain of g is all real numbers in the interval[-2,5], the domain off+gis all real numbers in the interval [0,5]

Step by step solution

01

Step 1. Given information 

If the domain of fis all real numbers in the interval [0,7]and the domain of g is all real numbers in the interval [-2,5], the domain off+g is all real numbers in the interval _________.

02

Step 2. Main Idea:

Domainoff+g=Domainoff鈭�Domainofg

03

Step 3. It is given that:

Domain of f=[0,7]

Domain of g=[-1,5]

Therefore,

f+g=[0,7]鈭�[-1,5]f+g=[0,5]

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In Problems 19-26,write the function whose graph is the graph of y=x3but is:

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Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.g(x)=x3-1

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