How to sketch $f(x)= |2x-1|-|1+3x|$

Question

How would you sketch $f(x)= |2x-1|-|1+3x|$? And how would you work out how to sketch it? Please help!

Plot for $x=-10, -9, \dots, 9,10$, join the dots, and ponder. — Gerry Myerson, Oct 02 '13 at 13:11
think where the function may behave "strangely" because of the absolute values — mau, Oct 02 '13 at 13:26

score 1 · Answer 1 · answered Oct 02 '13 at 13:16

We know that

$|x| = \begin{cases} x & x\ge 0 \\ -x & x\lt 0 \end{cases}$

Hence break up your domain into different regions where you can simply write down your function without the use of the absolute values (like above) and then it should be clear what to sketch.

score 1 · Answer 2 · answered Oct 02 '13 at 13:17

1

Step 1: Work out when $2x-1$ and $1+3x$ change signs.

Step 2: Using this information, write down the form of the equation in each region where both signs remain constant.

Step 3: Plot the result for each region.

answered Oct 02 '13 at 13:17

Glen O

12,425

How to sketch $f(x)= |2x-1|-|1+3x|$

2 Answers2