Question

How do you solve and graph `abs(m-2)<8`?

Answer 1

`f(m)={(m-10color(white)("xxx") {m:m>=2}),(-m-6color(white)("xxx") {m:m<2}):}`

for `dom f in (-oo,0)`

Explanation:

Recall that for a modulus function `f(x)=|x|`, `f(x)=x` for `x>=0` and `f(x)=-x` for `x<0`.

`|m-2| < 8`
`:. |m-2| - 8 < 0|`

If we call this a function

`f(m) = |m-2|-8` for `dom f in (-oo,0)`

then we can define it as a hybrid function, which follows the standard transformations of a function, we get:

`f(m)={((m-2)-8color(white)("xxx") {m:m>=2}),(-(m-2)-8color(white)("xxx") {m:m<2}):}`
`:. f(m)={(m-10color(white)("xxx") {m:m>=2}),(-m-6color(white)("xxx") {m:m<2}):}`

Of course, given the domain, we need only consider the function `g(m)=-m-6`, so to sketch, simply draw a straight line from the point `(0,-6)` remembering to leave an open circle at that coordinate.