Question

how do you write f(x)=|2x+1|+1 as a piecewise function?

Answer 1

oh i get to practice my piecewise in latex!

Answer 2

ok so
\[ |x| = \left\{\begin{array}{rcc}
x & \text{if} & x \geq 0 \\
- x & \text{if} & x < 0
\end{array}
\right.
\]

Answer 3

therefore
\[ |2x+1| = \left\{\begin{array}{rcc}
2x +1& \text{if} & 2x+1 \geq 0 \\
- 2x-1 & \text{if} & 2x+1 < 0
\end{array}
\right.
\]

Answer 4

but of course you want this in terms of x so you write
\[ |2x+1| = \left\{\begin{array}{rcc}
2x +1& \text{if} & x \geq -\frac{1}{2} \\
- 2x-1 & \text{if} & x <- \frac{1}{2}
\end{array}
\right.
\]

Answer 5

and so
\[ |2x+1| +1= \left\{\begin{array}{rcc}
2x +2& \text{if} & x \geq -\frac{1}{2} \\
- 2x & \text{if} & x <- \frac{1}{2}
\end{array}
\right.
\]

Answer 6

by adding one

Answer 7

wow thanks!!! so if y=|4x+1|+2x-3 then the pieccewise function would be...

Answer 8

|y|= 6x-2 if x\[\ge\] -1/4
-2x-4 if x\[>\]m1/4