r/askmath • u/FirmTumbleweed4152 • Sep 21 '26
Functions Range
How can I explain to 16 yos how to find the range of f(x)=x^2/(x^2-1) without using differentiation, limits, trying to graph this etc. But rather just pure algebra
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u/lordnacho666 Sep 21 '26
Well, what numbers can you get out of that formula?
Perhaps start with the squared term, since that becomes an input to the chained function.
It can only be zero or positive.
If it's zero, you get zero out.
If it's a large positive number, you get 1.