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range of (5x-x^2)/(x^4-25x^2)

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

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range 5x−x²x⁴−25x²

Solution

f(x)<0 or f(x)≥425

Interval Notation

(−∞ , 0)∪ [425 , ∞ )

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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 5x−x²x⁴−25x² : x<−5 or −5<x<0 or 0<x<5 or x>5

Simplify 5x−x²x⁴−25x² : −1x(x+5)

Extreme Points of −1x(x+5) : Minimum(−52 , 425 )

Find the range for the interval −∞ <x<−5: −∞ <f(x)<0

Find the range for the interval −5<x<0: 425 ≤ f(x)<∞

Find the range for the interval 0<x<5: −∞ <f(x)<−150

Find the range for the interval 5<x<∞ : −150 <f(x)<0

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

f(x)<0 or f(x)≥ 425 or f(x)<−150 or −150 <f(x)<0

f(x)<0 or f(x)≥ 425

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domain 5x−x²x⁴−25x²

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intercepts 5x−x²x⁴−25x²

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

range of (5x-x^2)/(x^4-25x^2)

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range of (5x-x^2)/(x^4-25x^2)

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