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Question 279637: True or False: The domain of f(x) = -|x| is all real numbers.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! true.
x can be any real number.
f(x) will always be negative, so the range of f(x) is equal to all real numbers smaller than or equal to 0.
regardless of what value you have for x, the absolute value of x will be greater than or equal to 0 and the negative of that will always be less than or equal to 0.
the domain is all real values of x (x can be positive or negative).
the range is all real values of x smaller than or equal to 0.
if x = 0, the absolute value of x = 0 and - the absolute value of 0 will be 0.
if x = -5, the absolute value of x will be 5 and minus that will be equal to -5.
if x = 5, the absolute value of x will be 5 and minus that will be equal to -5.
the absolute value sign surrounding x is part of the rules of the function and does not impact the domain.
the domain is the value of x only.
the absolute value sign is part of the rules of the equation that translate the domain into the range.
the minus sign is the other part of the rules of the equation that translate the domain into the range.
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