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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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: