Question

How do you write `y = | x - 2|` as piecewise functions?

Answer 1

See a solution process below:

Explanation:

Step 1) First, solve the term within the absolute value function for `0`:

`x - 2 = 0`

`x - 2 + color(red)(2) = 0 + color(red)(2)`

`x - 0 = 2`

`x = 2`

Step 2) Multiply the term within the absolute value function by `-1` and write a "less than" inequality with the result of Step 1:

`-1(x - 2) => -x + 2`

`y = -x + 2" for "x < 2`

Step 3) Take the term within the absolute value function and write a "greater than or equal to" inequality with the result of Step 1:

`y = x - 2" for "x >= 2`

Step 4) Combine Step 2 & Step 3 to form the piecewise function:

`y = {-x + 2" for "x < 2; x - 2" for "x >= 2}`

Answer 2

see below

Explanation:

`f: y=|x−2|`

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`f_1: y=x`
`f_2: y=|x|`
`f_3: y=|x-2|`

Absolute value mirrors every negative value to the positive according to x axis.
And finally, a number inside absolute value moves graph to the right or left. When it's minus:`|x-2|` then it moves to the right. You can remember it by finding zero point, which is 2 and it's greater than zero(on the right from zero). Now you should be able to make a graph