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Chapter 5: Q 114 (page 299)

In Problems 113-116, graph each function. Based on the graph, state the domain and the range and find any intercepts

114.f(x)=ln(-x)ifx鈮�-1-ln(-x)if-1<x<0

Short Answer

Expert verified

The domain is(-鈭�,0), the range is[0,鈭�)and the X- intercept is(-1,0).

Step by step solution

01

Step 1. Given information.

The following function is givenf(x)=ln-x:x鈮�鈥�-1,鈥�-ln-x:-1<鈥�x<鈥�0.

02

Step 2. Domain and range.

Domain of{ln(-x):x鈮�-1}:x鈮�-1

Domain of{-ln(-x):-1<x<0}:-1<x<0

Combine domains of all the pieces:

x鈮�-1

or -1<x<0

x<0

Extreme Points of {ln(-x):x鈮�-1,-ln(-x):-1<x<0}: Minimum (-1,0)

Find the range for the intervalrole="math" localid="1646940655792" -鈭�<x<-1:0<f(x)<鈭�

Find the range for the interval -1<x<0 :0<f(x)<鈭�

Combine the ranges of all domain intervals to obtain the function range

f(x)鈮�0or f(x)>0

X- axis interception points of {ln(-x):x鈮�-1,-ln(-x):-1<x<0}:(-1,0)

Y- axis interception point of {ln(-x):x鈮�-1,-ln(-x):-1<x<0}: None

X-Intercepts: (-1,0)

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