range of (|x|)/x

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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range |x|x

Solution

f(x)=−1 or f(x)=1

Interval Notation

f(x)=−1∪ f(x)=1

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Solution steps

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Function range definition

The set of values of the dependent variable for which a function is defined

Find the minimum and maximum value in each defined interval and unite the results

Domain of |x|x : x<0 or x>0

Extreme Points of |x|x : None

Absolute value functions are piecewise functions

Find the function intervals: x<0, x>0

Evaluate the function behavior for each interval

Find the range for the interval −∞ <x<0: f(x)=−1

Find the range for the interval 0<x<∞ : f(x)=1

Combine the ranges of all domain intervals to obtain the function range

f(x)=−1 or f(x)=1

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domain |x|x

vertices |x|x

intercepts |x|x

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Notebook

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

range of (|x|)/x

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