Absolute value expressions as piecewise expressions?

Write the following absolute value expressions as piecewise expressions:

|x^2-1|

|x^2+x-12|

|x^2+4x+4|

(If you can show me how to do one, I’ll figure out the other 2!)

Top 2 Answers

A few days ago

hayharbr

Favorite Answer

First find where each one equals zero. That defines the starting points for each piece. Example:

x^2 + x – 12 = (x + 4)(x – 3) and equals zero if x = -4 or 3

So the pieces are: x < -4, -4 < x < 3, and x > 3 [with two of the inequalities including = so -4 and 3 aren’t left out]

Now, if x , -4, both parts are negative so the product is positive and the absolute value bars make no difference. Similarly if x > 3 both are positive and again they don’t change it. But in between (x-3) is negative while (x + 4) is positive so the absolute value changes its sign.

Answer: (with the big curly brace)

x^2 + x – 12 if x >= 3 or x <= -4 -(x^2 + x - 12) if -4 < x < 3

5 years ago

See where they equal zero, then do the positive value to the right of there and the negative value to the left. Like the first one equals zero if x = 2 so y = 2x – 4, x ≥ 2 y = – (2x – 4) [or -2x + 4] , x < 2

what is 6/8 divided 8 5/7 ? please help?

need ideas?

What are some similarities and diffrences between Marilyn Manson and the Miller from the Canterbury Tales?

I need someone to correct my english paper…?

around what time period were the tigres and euphrates rivers used? also indus and ganges? huang he &yangtze ?

What is the relationships between Mendel’s Law of Segretation and the movement of chromosomes in meiosis?

what are the contributions of henri gantt to scientific management?

Mathematical thinking?

Absolute value expressions as piecewise expressions?

Absolute value expressions as piecewise expressions?

Related Posts