What is the y=((x+1)(3x-2))/((x-1)(x+4)) ?

The y=((x+1)(3x-2))/((x-1)(x+4)) is

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y=((x+1)(3x-2))/((x-1)(x+4))

y = \frac{( x + 1 ) ( 3 x - 2 )}{( x - 1 ) ( x + 4 )}

Domain : x < - 4 or - 4 < x < 1 or x > 1

Range : f (x) \leq \frac{- 4 21 + 31}{25} or f (x) \geq \frac{4 21 + 31}{25}

X Intercepts : (- 1, 0), (\frac{2}{3}, 0), Y Intercepts : (0, \frac{1}{2})

Asymptotes : Vertical x = - 4, x = 1, Horizontal y = 3

Extreme Points : Maximum (\frac{5 - 21}{4}, \frac{31 - 4 21}{25}), Minimum (\frac{5 + 21}{4}, \frac{31 + 4 21}{25})

Interval Notation

Domain : (- \infty, - 4) \cup (- 4, 1) \cup (1, \infty)

Range : (- \infty, \frac{- 4 21 + 31}{25}] \cup [\frac{4 21 + 31}{25}, \infty)

Solution steps

Domain of

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

Range of

\frac{( x + 1 ) ( 3 x - 2 )}{( x - 1 ) ( x + 4 )} : f (x) \leq \frac{- 4 21 + 31}{25} or f (x) \geq \frac{4 21 + 31}{25}

Axis interception points of

\frac{( x + 1 ) ( 3 x - 2 )}{( x - 1 ) ( x + 4 )} :

X Intercepts

: (- 1, 0), (\frac{2}{3}, 0),

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

\frac{( x + 1 ) ( 3 x - 2 )}{( x - 1 ) ( x + 4 )} :

Vertical

: x = - 4, x = 1,

Horizontal

: y = 3

Extreme Points of

\frac{( x + 1 ) ( 3 x - 2 )}{( x - 1 ) ( x + 4 )} :

Maximum

(\frac{5 - 21}{4}, \frac{31 - 4 21}{25}),

Minimum

(\frac{5 + 21}{4}, \frac{31 + 4 21}{25})

y = 2 x^{2} + 12 x + 17

f (x) = 144 + x^{2}

f (t) = 20 cos (36 t) cos (6 t)

y = sin (3 x^{2})

f (x) = e^{- \frac{2}{x}}