Question

If $f=\left\{\right(1,1),(2,3),(0,-1),(-1,-3\left)\right\}$ be a linear function $z$ to $z$, find $f\left(x\right).$

• A. $2x+1$
• B. $2x-1$
• C. $3x+2$
• D. $3x-1$

Answer 1

Answer: (B)

$2x-1$

If $f=\left\{\right(1,1),(2,3),(0,-1),(-1,-3\left)\right\}$ be a linear function $z$ to $z.$

By $two$ points $(1,1)$ & $(2,3)$ we can draw a linear equation.

$(y-1)=\frac{3-1}{2-1}(x-1)$

$y-1=\frac{2}{1}(x-1)$

$y-1=2x-2$

$y+2-1=2x$

$y-2x+1=0$

$y=2x-1$

Hence linear function will be $f\left(x\right)=2x-1.$