Definition of Absolute Value of a Function

Homework Statement

Question straight off the book "In this lesson, you have explored the absolute value of a function. How is it defined?"

Homework Equations

In this lesson, I did questions like xE[0,9] and was told to write each intervals in absolute value notation.

The Attempt at a Solution

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Integral
Staff Emeritus
Gold Member
Start by showing us what definition of Absolute value you are working with?

berkeman
Mentor
The absolute value just means the value as a positive quantity. If you take the absolute value of a negative quantity, you get the corresponding positive quantity. Like, |-5| = 5.

I don't understand the notation xE[0,9], however, and writing an "interval in absolute value notation" doesn't make much sense to me. An interval is traditionally a subset of the independent axis, while the function over that interval is plotted on the dependent axis. Can you clarify?

xE[0,9] is an example of interval notation, read "x is an element of the closed interval from 0 to 9". It sounds like your book wants the piecewise definition. Ill give you a hint, the 2 cases are x>0 and x<0

berkeman
Mentor
xE[0,9] is an example of interval notation, read "x is an element of the closed interval from 0 to 9".
Oh, I get it now. Thanks. It was the use of a standard letter "E" that fooled me. I'd use the \in function in LaTex:

$$x \in [0,9]$$