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Domain and Range of absolute value of X
- Thread starter lillianal
- Start date
what are the domain and range of Y > |X|?
What are the domain and range of Y < |X|?
Domain: The values X can take
Range: The values Y can take
So, what is the dividing line (literally in this case) between the regions. Generally greater than can be interpreted as 'above the line' and less than can be interpreted as 'below the line'.
Hint: If x was between 0 and ∞, inclusive, could y ever be zero? Is y limited in the value it can take, either below or above?
Range/Domain of Absolute Value Inequalities
Say that the vetex was at minus 3, shaded above. The domain would seem to be all real numbers, but the range would be -3 < Y.
However, below the line, it would seem that the domain was all real numbers, and the range would also be. However, the domain below the line doesn't include the area above the line for absolute value inequalities, so it would seem that ARN for both domain and range couldn't be correct.
Comments?
Say that the vetex was at minus 3, shaded above. The domain would seem to be all real numbers, but the range would be -3 < Y.
However, below the line, it would seem that the domain was all real numbers, and the range would also be. However, the domain below the line doesn't include the area above the line for absolute value inequalities, so it would seem that ARN for both domain and range couldn't be correct.
Comments?
Domain: The values X can take
Range: The values Y can take
So, what is the dividing line (literally in this case) between the regions. Generally greater than can be interpreted as 'above the line' and less than can be interpreted as 'below the line'.
Hint: If x was between 0 and ∞, inclusive, could y ever be zero? Is y limited in the value it can take, either below or above?
Say that the vetex was at minus 3, shaded above. The domain would seem to be all real numbers, but the range would be -3 < Y.
However, below the line, it would seem that the domain was all real numbers, and the range would also be. However, the domain below the line doesn't include the area above the line for absolute value inequalities, so it would seem that ARN for both domain and range couldn't be correct.
Comments?
You seem to have the y > |x| down but, for both cases, the domain is not above or below, range is above or below. Domain is left or right if there is a restriction. There is no restriction on x, so the domain is ARN in both cases.
For y < |x|, any negative number is less than |x|, no matter what x is. So all negative numbers belong to the range of y < |x|. Suppose x were 100, then any y number less than 100 would satisfy y < |100|. What if x were 1000, 10000, 100000, .... So the range of y < |x| is all real numbers. That is the shaded region above is excluded, NOT the numbers in the shaded region.