Find the domain and sketch the graph of G(x) = (3x + |x|)/x

The absolute value of a number |x|, is defined as `|x| = x, x>= 0` and `|x| = -x, x < 0` . The function `G(x) = (3x+|x|)/x` can be rewritten for different values of x as: `G(x) = (3x + x)/x, x > 0` = `(4x)/x, x > 0` = `4, x > 0` When x = 0, `G(x) = (3x + x)/x = 0/0` which is indeterminate. `G(x) = (3x - x)/x, x < 0` = `(2x)/x, x < 0` = `2, x <0` The value of G(x) is real and defined for all values of x except 0. The domain of the function is R - {0} The graph of this function is: <embed type="image/svg+xml" src="/js/tinymce/js/tinymce/plugins/asciisvg/js/d.svg" style="width: 300px; height: 200px; vertical-align: middle; float: none;" sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,(4x)/x,null,2,0,0,20,black,1,none,func,(2x)/x,null,0,2,-10,0,black,1,none" />

Homework Help > Math

Find the domain and sketch the graph of G(x) = (3x + |x|)/x

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on May 5, 2015 at 4:54 AM

The absolute value of a number |x|, is defined as `|x| = x, x>= 0` and `|x| = -x, x < 0` .

The function `G(x) = (3x+|x|)/x` can be rewritten for different values of x as:

`G(x) = (3x + x)/x, x > 0`

= `(4x)/x, x > 0`

= `4, x > 0`

When x = 0, `G(x) = (3x + x)/x = 0/0` which is indeterminate.

`G(x) = (3x - x)/x, x < 0`

= `(2x)/x, x < 0`

= `2, x <0`

The value of G(x) is real and defined for all values of x except 0.

The domain of the function is R - {0}

The graph of this function is: