Functions: Domain and range
Range
Take a look at the function #f(x)=x^2#.
We see that the smallest value this function takes on is #0#, after that the function increases indefinitely.
Hence all values in the interval #\ivco{0}{\infty}# are within range of the function.
We say that the range of #f# is equal to the interval #\ivco{0}{\infty}#.
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Range
The range of a function #f# consists of all values #f(x)# that this function can reach on its domain.
Example
Determine the range of #f(x)=-x^2#:
the interval #(-\infty, 0]#
The range is: #\ivco{-7}{\infty}#
We sketch the graph:
We can read the range from the sketch.
The smallest function value is #-7# and after that the graph increases indefinitely.
The range is: #\ivco{-7}{\infty}#.
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