What is the f(x)=((x+3)^2-(x-1)^2)/(4x^2-4x-8) ?

The f(x)=((x+3)^2-(x-1)^2)/(4x^2-4x-8) is

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f(x)=((x+3)^2-(x-1)^2)/(4x^2-4x-8)

f (x) = \frac{( x + 3 ) ^{2} - ( x - 1 ) ^{2}}{4 x ^{2} - 4 x - 8}

Domain : x < - 1 or - 1 < x < 2 or x > 2

Range : f (x) < - \frac{2}{3} or - \frac{2}{3} < f (x) < 0 or f (x) > 0

Y Intercepts : (0, - 1)

Asymptotes : Vertical x = 2, Horizontal y = 0

Extreme Points : None

Interval Notation

Domain : (- \infty, - 1) \cup (- 1, 2) \cup (2, \infty)

Range : (- \infty, - \frac{2}{3}) \cup (- \frac{2}{3}, 0) \cup (0, \infty)

Solution steps

Domain of

\frac{( x + 3 ) ^{2} - ( x - 1 ) ^{2}}{4 x ^{2} - 4 x - 8} : x < - 1 or - 1 < x < 2 or x > 2

Range of

\frac{( x + 3 ) ^{2} - ( x - 1 ) ^{2}}{4 x ^{2} - 4 x - 8} : f (x) < - \frac{2}{3} or - \frac{2}{3} < f (x) < 0 or f (x) > 0

Axis interception points of

\frac{( x + 3 ) ^{2} - ( x - 1 ) ^{2}}{4 x ^{2} - 4 x - 8} :

Y Intercepts

: (0, - 1)

Asymptotes of

\frac{( x + 3 ) ^{2} - ( x - 1 ) ^{2}}{4 x ^{2} - 4 x - 8} :

Vertical

: x = 2,

Horizontal

: y = 0

Extreme Points of

\frac{( x + 3 ) ^{2} - ( x - 1 ) ^{2}}{4 x ^{2} - 4 x - 8} :

None

f (x) = - 0.5 x^{2} + 20 x - 100

f (x) = - 0.25 x^{2} + 40 x + 300

f (x) = \frac{- x + 10}{x ^{3}}

f (x) = 4 + ln (x)

f (x) = - 0.05 x^{2} + 20 x + 1000

What is the f(x)=((x+3)^2-(x-1)^2)/(4x^2-4x-8) ?
The f(x)=((x+3)^2-(x-1)^2)/(4x^2-4x-8) is