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# Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ a function?If g is described by $g(x)=\alpha x+\beta$,then what value should be assigned to $\alpha\;and\;\beta.$

$\begin{array}{1 1} \alpha =1 \qquad \beta =-1 \\ \alpha =2 \qquad \beta =-1 \\ \alpha =2 \qquad \beta =-2 \\ \alpha =-1 \qquad \beta =-1 \end{array}$

Toolbox:
• We find values for $\alpha$ and $\beta$ such that $b=\alpha a+\beta$ for all or ordered pairs $(a,b) \in g$
$g=\{(1,1),(2,3),(3,5)(4,7)\}$ is a function

we see that

If $g(x)=2x-1$ is satisfied for all values of $x =\{1,2,3,4\}$

$g(1)=2 \times 1-1=1$

$g(2)=2 \times 2-1=3$

$g(3)=2 \times 3-1=5$

$g(4)=2 \times 4-1=7$

Hence $\alpha =2 \qquad \beta =-1$