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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Graphing Logarithmic Functions In Exercises 13-20, sketch the graph of the function. See Example 1.

y = 1 2 ln | 2 x |

To determine

To graph: The function y=12ln|2x|.

Explanation

Given Information:

The provided function is y=12ln|2x|.

Graph:

Consider the function, y=12ln|2x|

The natural logarithmic function is defined only for positive values, so the domain of the function, y=12ln|2x| is |2x|>0 or |x|>0 which means x>0 or x<0.

As the domain is |x|>0, then take the value of x greater or less than 0.

To draw the graph of y=12ln|2x|, first compute the value of y for different values of x.

Compute the value of y at x=1.5 by substituting x=1.5 in the equation y=12ln|2x| as,

y(1.5)=12ln|2(1.5)|=12ln|3|=1.0982=0.549

Compute the value of y at x=1 by substituting x=1 in the equation y=12ln|2x| as,

y(1)=12ln|2(1)|=12ln|2|=0.69312=0.347

Compute the value of y at x=0.5 by substituting x=0.5 in the equation y=12ln|2x| as,

y(0.5)=12ln|2(0.5)|=12ln|1|=0

Compute the value of y at x=0.5 by substituting x=0.5 in the equation y=12ln|2x| as,

y(0

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