Defined on the set of real numbers R, $$\begin{aligned}
& \beta _ { 1 } = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } = 1 \right\} \\
& \beta _ { 2 } = \left\{ ( x , y ) : x ^ { 2 } + y = 2 \right\} \\
& \beta _ { 3 } = \left\{ ( x , y ) : x - y ^ { 2 } = 3 \right\}
\end{aligned}$$ Which of these relations define a function of the form $\mathbf { y } = \mathbf { f } ( \mathbf { x } )$ on $R$? A) Only $\beta _ { 1 }$ B) Only $\beta _ { 2 }$ C) $\beta _ { 1 }$ and $\beta _ { 3 }$ D) $\beta _ { 2 }$ and $\beta _ { 3 }$ E) $\beta _ { 1 } , \beta _ { 2 }$ and $\beta _ { 3 }$
Defined on the set of real numbers R,
$$\begin{aligned}
& \beta _ { 1 } = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } = 1 \right\} \\
& \beta _ { 2 } = \left\{ ( x , y ) : x ^ { 2 } + y = 2 \right\} \\
& \beta _ { 3 } = \left\{ ( x , y ) : x - y ^ { 2 } = 3 \right\}
\end{aligned}$$
Which of these relations define a function of the form $\mathbf { y } = \mathbf { f } ( \mathbf { x } )$ on $R$?\\
A) Only $\beta _ { 1 }$\\
B) Only $\beta _ { 2 }$\\
C) $\beta _ { 1 }$ and $\beta _ { 3 }$\\
D) $\beta _ { 2 }$ and $\beta _ { 3 }$\\
E) $\beta _ { 1 } , \beta _ { 2 }$ and $\beta _ { 3 }$