Let f be the function from x ={0, 1, 2, 3, 4, 5} to X defined by f(x) = 4x mod 6. Write f as a set of ordered pairs and draw the arrow diagram of f . Is f one-to-one? Is f onto?

It is given that $x=\{0,1,2,3,4,5\}.$

$f(0)=4(0)\mod 6=0$

$f(1)=4(1)\mod 6=4$

$f(2)=4(2)\mod 6=2$

$f(3)=4(3)\mod 6=0$

$f(4)=4(4)\mod 6=4$

$f(5)=4(5)\mod 6=2$

The given function as the set of ordered pairs

$f = \{(0,0), (1,4), (2,2), (3,0), (4,4), (5,2)\}$

Picture below represents arrow diagram of $f$

The function is called one-to-one if each $x$ from the domain has exactly one image in the range, and no $y$ in the range is image of more than one $x$ from the domain. As we can see, is the image of both and $3,$ so the function is not one-to-one.

The function is called onto if every $y$ in the range is the image of at least one $x$ from the domain. As we can see from diagram above, this function is onto.