I am working on basic functions, I am asked is x-5=y^2 a function,

Question

i use the square root property and get plus or minus the sqaure root of x-5=y, then I come to my question, for any value of x greater than 5, how many values of y result? I need some insight to fully understand this please.

Answer 1

Relation $R=\left\{ \left(x,y\right)\in\mathbb{R}^{2}\mid x-5=y^{2}\right\} $ is not a function. If it would be then for every $x\in\mathbb{R}$ there should be a unique $y\in\mathbb{R}$ such that $x-5=y^{2}$ wich is not the case. For $x<5$ there is no such $y$ and for $x>5$ there are more than one.

Relations $f=\left\{ \left(x,y\right)\in[5,\infty)\times[0,\infty)\mid x-5=y^{2}\right\} $ and $g=\left\{ \left(x,y\right)\in[5,\infty)\times(-\infty,0]\mid x-5=y^{2}\right\} $ are functions.

They do have the required property.