Use the definition of absolute value to write f as a piecewise-defined function

we are given

any absolute function

Let's assume that function as

f(x)=|x|

now, we can write it in piecwise form

we know that value of f(x) will always be positive

so, we write function such that it results in positive value

so, we can write as

...........Answer

If you have two negatives they cancel each other out and make a positive. The  same if you have to positives the product will be positive. If you have a negative and a positive you multiply the numbers and bring down the negative. Same if you have a positive and a negative. Only two negatives cancel each other out, same with positives. For example -4(-5)(-1) you would use order of operations, 4 and the 5 cancel each other out and you multiply 20 by -1 which is -20 since you bring down the negative.