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Popular >

y=((x^2-4x+1))/((x^2+4x+1))

Solution

y = \frac{( x ^{2} - 4 x + 1 )}{( x ^{2} + 4 x + 1 )}

Solution

Domain : x < - 2 - 3 or - 2 - 3 < x < - 2 + 3 or x > - 2 + 3

Range : f (x) \leq - 3 or f (x) \geq - \frac{1}{3}

X Intercepts : (2 + 3, 0), (2 - 3, 0), Y Intercepts : (0, 1)

Asymptotes : Vertical x = - 2 - 3, x = - 2 + 3, Horizontal y = 1

Extreme Points : Maximum (- 1, - 3), Minimum (1, - \frac{1}{3})

+1

Solution steps

Domain of

\frac{x ^{2} - 4 x + 1}{x ^{2} + 4 x + 1} : x < - 2 - 3 or - 2 - 3 < x < - 2 + 3 or x > - 2 + 3

Range of

\frac{x ^{2} - 4 x + 1}{x ^{2} + 4 x + 1} : f (x) \leq - 3 or f (x) \geq - \frac{1}{3}

Axis interception points of

\frac{x ^{2} - 4 x + 1}{x ^{2} + 4 x + 1} :

X Intercepts

: (2 + 3, 0), (2 - 3, 0),

Y Intercepts

: (0, 1)

Asymptotes of

\frac{x ^{2} - 4 x + 1}{x ^{2} + 4 x + 1} :

Vertical

: x = - 2 - 3, x = - 2 + 3,

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} - 4 x + 1}{x ^{2} + 4 x + 1} :

Maximum

(- 1, - 3),

Minimum

(1, - \frac{1}{3})

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f (s) = \frac{36}{( s ^{2} + 1.2 s + 36 )}

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Frequently Asked Questions (FAQ)

What is the y=((x^2-4x+1))/((x^2+4x+1)) ?
The y=((x^2-4x+1))/((x^2+4x+1)) is