Question

write the absolute value function as a piecewise function. y=I4x+1I+2x-3

Answer 1

The function \(y = |x|\) as a piecewise function can be written as...\[f(x) = \cases{x ~ {\rm \quad if ~}x \ge 0 \\ -x \quad {\rm if~}x < 0 }{}\]I guess that says a lot?

Answer 2

Still, for clarity, the function \(y = |7x + 8|\) can be written as\[f(x) = \cases{7x + 8 ~ {\rm \quad if ~}7x +8 \ge 0 \\ -(7x + 8) \quad {\rm if~}7x +8< 0 }{}\]

Answer 3

Getting it?

Answer 4

yes thanks that helps a lot! i understand how the absolute value works as a piecewise function but how do you add the second half? is that just added on the end of both???