Question

If the function $f:\{-3,-2,-1,0,1,2,3\}\to \{0,1,2,3,4,5\}$ is defined as $f\left(x\right)=|x-1|$, then the number of elements in the range of $f$ is

Answer 1

$f:\{-3,-2,-1,0,1,2,3\}\to \{0,1,2,3,4,5\}$
$f\left(x\right)=|x-1|$
We find the image of $-3,-2,-1,0,1,2,3$ under $f$.
$f(-3)=|-3-1|=|-4|=4$
$f(-2)=3,f(-1)=2,f\left(0\right)=1,f\left(1\right)=0,f\left(2\right)=1,f\left(3\right)=2$
$\therefore$ Range of function is $\{0,1,2,3,4\}$
Number of elements in range is $5$.