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Popular >

f(x)=(x^2-16)/(x^2-x-6)

Solution

f (x) = \frac{x ^{2} - 16}{x ^{2} - x - 6}

Solution

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

Range : f (x) \leq \frac{- 4 21 + 44}{25} or f (x) \geq \frac{4 21 + 44}{25}

X Intercepts : (4, 0), (- 4, 0), Y Intercepts : (0, \frac{8}{3})

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

Extreme Points : Minimum (2 (5 - 21), \frac{4 ( 11 + 21 )}{25}), Maximum (2 (5 + 21), \frac{4 ( 11 - 21 )}{25})

+1

Interval Notation

Domain : (- \infty, - 2) \cup (- 2, 3) \cup (3, \infty)

Range : (- \infty, \frac{- 4 21 + 44}{25}] \cup [\frac{4 21 + 44}{25}, \infty)

Solution steps

Domain of

\frac{x ^{2} - 16}{x ^{2} - x - 6} : x < - 2 or - 2 < x < 3 or x > 3

Range of

\frac{x ^{2} - 16}{x ^{2} - x - 6} : f (x) \leq \frac{- 4 21 + 44}{25} or f (x) \geq \frac{4 21 + 44}{25}

Axis interception points of

\frac{x ^{2} - 16}{x ^{2} - x - 6} :

X Intercepts

: (4, 0), (- 4, 0),

Y Intercepts

: (0, \frac{8}{3})

Asymptotes of

\frac{x ^{2} - 16}{x ^{2} - x - 6} :

Vertical

: x = - 2, x = 3,

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} - 16}{x ^{2} - x - 6} :

Minimum

(2 (5 - 21), \frac{4 ( 11 + 21 )}{25}),

Maximum

(2 (5 + 21), \frac{4 ( 11 - 21 )}{25})

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Frequently Asked Questions (FAQ)

What is the f(x)=(x^2-16)/(x^2-x-6) ?
The f(x)=(x^2-16)/(x^2-x-6) is