How do you find domain and range for # f(x) =abs(2x+1)#?

1 Answer
marfre
Jul 2, 2018

See answer below

Explanation:

Given: #f(x) = |2x + 1|#

To find the domain and range analytically, you would need to know that an absolute value only allows positive values for the output.

Any #x# value selected would only give zero or positive values for #y#. This means

The domain is the valid inputs: #x: " all Reals"#

The range is the valid outputs: #y, " "y >= 0#

You can also find the domain and range by graphing the function and seeing that there are no negative #y# values. This means the range would be # " "y >= 0#

graph{abs(2x+1) [-5, 5, -5, 5]}

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