mariah wrote:For which of the following functions F(a+b)=F(a)+F(b) for all positive numbers a and b?

F(x)=x^2 ;
F(x)=x+1
F(x)=x^(1/2)
F(x)=2/x
F(x)=-3x

I am in trouble with functions

A LOT of students have trouble with function notation.
There is an algebraic approach to this question, but it takes longer than the approach of plugging in numbers. Let a and b both equal 1

So, the question becomes, "Which of the following functions are such that f(1+1) = f(1) + f(1)?"
In other words, for which function does f(2) = f(1) + f(1)?

A) If f(x)=x^2, does f(2) = f(1) + f(1)?
Plugging in 2 and 1 we get: 2^2 = 1^2 + 1^2 (doesn't work)
So, it is not the case that f(2) = f(1) + f(1), when f(x)=x^2

B) If f(x)=x+1, does f(2) = f(1) + f(1)?
Plugging in 2 and 1 we get: 2+1 = 1+1 + 1+1
No, it is not the case that f(2) = f(1) + f(1)
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Keep trying each function (none works until we get to E)
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E) If f(x)=-3x, does f(2) = f(1) + f(1)?
Plugging in 2 and 1 we get: (-3)(2) = (-3)(1) + (-3)(1)
Yes, it works
If f(x)=-3x, f(2) = f(1) + f(1)

The correct answer is E