Question

Find an algebraic model for the sum of a number and its reciprocal.

I have come up with y=x+ (1/x), although I was wondering if it would be correct to write it as y=x^2+1/x

I am supposed to graph this, but when i graph both I get different graphs on my graphing calculator.

Please help me understand why.

Answer 1

Your first answer, y = x + (1/x), is absolutely right.

I don't understand why you would think that a square would be involved. Bringing in the square makes it a completely different thing, and that's why you're getting different results on your graphing calculator.

Consider the number 3. The sume of that number with its reciprocal is

3 + 1/3.

The sum of its square with its reciprocal would be 9 + 1/3, which is obviously quite a different number!