Question

Let $f=\left\{\right(1,1),(2,3),(0,-1),(-1,-3\left)\right\}$ be a function described by the formula $f\left(x\right)=ax+b$ for some integers $a,b$. Determine $a,b$.

• A. $a=2,b=-1$
• B. $a=1,b=0$
• C. $a=0,b=-1$
• D. None of these

Answer 1

The correct option is A $a=2,b=-1$

$f\left(1\right)=1,f\left(2\right)=3,f\left(0\right)=-1$ and $f(-1)=-3$.

It is given that $f\left(x\right)=ax+b$. Therefore,

$f\left(1\right)=1$ and $f\left(2\right)=3⟹a+b=1$ and $2a+b=3$

$a=2,b=-1$

Substituting the values of a and b in $f\left(x\right)=ax+b$, we get, $f\left(x\right)=2x+1$.

$f\left(0\right)=-1,f(-1)=-3$ are true.

Hence, $a=2$ and $b=-1$