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Chapter 5: Q 113 (page 299)

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

113.f(x)=ln(-x)ifx<0=ln(x)ifx>0

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

The following function is givenf(x)=ln(-x)ifx<0=ln(x)ifx>0.

02

Step 2. The range and domain.

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

Domain of {ln(x):x>0}:x>0

Hence, the domain is (-鈭�,0)鈭�(0,鈭�).

Extreme Points of {ln(-x):x<0,ln(x):x>0}: None

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

Find the range for the interval0<x<鈭�:-鈭�<f(x)<鈭�

Combine the ranges of all domain intervals to obtain the function range -鈭�<f(x)<鈭�

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

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

X Intercepts: (-1,0),(1,0)

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