值域 |x|(x^3-2x)

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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|(x³−2x)

Solution

−∞ <f(x)<∞

Interval Notation

(−∞ , ∞ )

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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|(x³−2x) : −∞ <x<∞

Extreme Points of |x|(x³−2x): Maximum(−1, 1), Saddle(0, 0), Minimum(1, −1)

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<∞ : −1≤ f(x)<∞

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

f(x)≤ 1 or f(x)≥ −1

−∞ <f(x)<∞

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domain |x|(x³−2x)

vertices |x|(x³−2x)

intercepts |x|(x³−2x)

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

值域 |x|(x^3-2x)

Solution

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