Question

writing piecewise functions?
f(x)=abs(2x)-abs(x-2)+3

Answer 1

\[f(x)=\left| 2x \right|-\left| x-2 \right|+3\]

Answer 2

this function can be broken into 3 pieces

Answer 3

i know that much...and dont you write one as it is and the other with the negative sign?

Answer 4

- when \(\large x<0\) ... both (2x) and(x-2) are negative
- when \(\large 0\le x < 2\) ... (x-2) is negative but (2x) is not
- and when \(\large 2\le x\) ... both (2x) and(x-2) are not negative

Answer 5

oh okay and how did you find which one is negative and which one isnt?

Answer 6

if 2x is negative
\[\large \implies 2x < 0 \]\[\large \implies x < 0 \]

if (x-2) is negative
\[\large \implies x-2 < 0 \]\[\large \implies x-2+2 < 0+2 \]\[\large \implies x < 2 \]

Answer 7

whenever something inside the absolute value is negative you flip its sign.

Answer 8

oh i understand now thank you:)

Answer 9

ok.. thanks for the medal