sketch the following funciton and state the domain and range. y= 1/2 Sqr root ( 2x+4 ) -3  Please explain the domain and range with a little detailed concept. Thanks

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taylormath | High School Teacher | (Level 2) Adjunct Educator

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The domain of a function represents the input values.  Here the domain stands for the x-values. Since the square root of a negative does not exist in the real number system, 2x+4 must be greater than or equal to 0. So the domain is found by solving the inequality:

`2x+4>=0`

`2x>=-4`

`x>=-2`

The allowable x-values must be greater than or equal to -2.

The range represents the output of the function.  Here the range stands for the y-values. Since x=-2 is the smallest value of x, the smallest value for y is found by:

y=1/2 sqrt (2(-2)+4) - 3

y=1/2 sqrt (0) - 3

y=-3

The range of the function is `y>=-3`

Here is a graph that shows the graph exists for x's greater than or equal to -2 and y's greater than or equal to -3.

 

 

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