Question

What is the graph of the function f(x) = the quantity of x squared minus 7 x plus 12, all over x minus 3

Answer 1

The given function is
`y=(\left(x^2-7x+12\right))/(x-3)`

factor the
`x^2-7x+12`

Re- write above as,

`x^2-4x-3x+12`

`x(x-4)-3(x-4)`

`(x-4)(x-3)`

The function as:

`y=((x-4)(x-3))/(x-3)`

and simplifies to

f(x) = x -4 . . . . . . . . x ≠ 3

The graph is straight line y = x-4, with a hole at x=3.

The graph is shown in figure-1