Define a Relation $R$ From $\mathbf { R }$ To $\mathbf { R }$

question 6

Essay

Define a relation $R$ from $\mathbf { R }$ to $\mathbf { R }$ as follows: For all $( x , y ) \in \mathbf { R } \times \mathbf { R } , ( x , y ) \in R$ if, and only if, $x = y ^ { 2 } + 1$ .
(a) Is $( 2,5 ) \in R$ ? Is $( 5,2 ) \in R$ ? Is (-3) $R$ 10? Is $10 R ( - 3 )$ ?
(b) Draw the graph of $R$ in the Cartesian plane.
(c) Is $R$ a function from $\mathbf { R }$ to $\mathbf { R }$ ? Explain.

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