Question

A $=[-1,1]$. B $=[0,1]$, C $=[-1,0]$
$S_1=\left\{\right(x,y)|x^2+y^2=1,xϵA,yϵA\}$
$S_2=\left\{\right(x,y)|x^2+y^2=1,xϵA,yϵB\}$
$S_3=\left\{\right(x,y)|x^2+y^2=1,xϵA,yϵC\}$
$S_4=\left\{\right(x,y)|x^2+y^2=1,xϵB,yϵC\}$

• A. $S_1$ is not a graph of a function
• B. $S_2$ is not a graph of a function
• C. $S_3$ is not a graph of a function
• D. $S_4$ is not a graph of a function

Answer 1

The correct option is A $S_1$ is not a graph of a function

The concept of graph is that "A set of points in the plane is the graph of a function if and only if no vertical line intersects the graph in more than one point."

Here $S_1$ is not a graph of a function as there is a vertical line which cuts the circle in more than one points these points are $(0,1)$ and $(0,-1)$ and the vertical line is the $y$-axis. (This method is called vertical line test)

But $S_2,S_3,S_4$ are graphs of a function by vertical line test.