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Two young mathematicians examine one (or two!) functions.
Check out this dialogue between two calculus students (based on a true
Riley, I have a pressing question.
Tell me. Tell me everything.
Think about the function
Is this function equal to ?
Well if I plot them with my calculator, they look the same.
And I suppose if I write
Sure! But what about when ? In this case
Right, is undefined because we cannot divide by zero. Hmm. Now I see the
In the context above, are and the same function?
Suppose and are functions but the domain of is different from the domain
of . Could it be that and are actually the same function?
The domain of a function is part of the “data” of the function. A function is not a
rule for transforming the input to the output, but rather the relationship between a
specified collection of inputs (the domain) and possible outputs (the range).
Can the same function be represented by different formulas?
Are and the same function?
These are the same function although they are represented by different
formulas.These are different functions because they have different formulas.
Let and . The domain of each of these functions is all real numbers. Which of the
following statements are true?
There is not enough information to determine if .The functions are equal.If , then .We have since uses the variable and uses
the variable .