indices

[red and white kop!]

i am supposed to sketch the function x^(2/3) - x^(-2/3)
is there any general rule for sketching functions of this form, i.e. involving the addition or subtraction of the same variable with different indices?

 

[mmm4444bot]

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is there any general rule for sketching functions of this form Umm, use graph paper ?

Hmmm. A singular rule.

Nope.

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But, we can use our "toolkit" of skills and knowledge, to obtain the basic behavior. After that, a small table of xy-values can help to confirm it.

Consider domain

Consider asymptotes

Test for even or odd function

Understand rational exponents

Have familiarity with basic radical-function graphs

Analyze ratio-value changes for |x| < 1

Analyze global behavior

(Off the top of my head, probably missed listing some things)

The main point: We need to drive, to work, even in a red and white kop

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[red and white kop!]

i didnt catch that thing about driving and working but i guess, you know, whatever makes you happy