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Popular >

y=((x^2+x-12))/((x^2-4))

Solution

y = \frac{( x ^{2} + x - 12 )}{( x ^{2} - 4 )}

Solution

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

Range : f (x) \leq - \frac{15}{4} + 2 or f (x) \geq \frac{15}{4} + 2

X Intercepts : (3, 0), (- 4, 0), Y Intercepts : (0, 3)

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

Extreme Points : Minimum (2 (4 - 15), \frac{8 + 15}{4}), Maximum (2 (4 + 15), \frac{8 - 15}{4})

+1

Interval Notation

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

Range : (- \infty, - \frac{15}{4} + 2] \cup [\frac{15}{4} + 2, \infty)

Solution steps

Domain of

\frac{x ^{2} + x - 12}{x ^{2} - 4} : x < - 2 or - 2 < x < 2 or x > 2

Range of

\frac{x ^{2} + x - 12}{x ^{2} - 4} : f (x) \leq - \frac{15}{4} + 2 or f (x) \geq \frac{15}{4} + 2

Axis interception points of

\frac{x ^{2} + x - 12}{x ^{2} - 4} :

X Intercepts

: (3, 0), (- 4, 0),

Y Intercepts

: (0, 3)

Asymptotes of

\frac{x ^{2} + x - 12}{x ^{2} - 4} :

Vertical

: x = - 2, x = 2,

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} + x - 12}{x ^{2} - 4} :

Minimum

(2 (4 - 15), \frac{8 + 15}{4}),

Maximum

(2 (4 + 15), \frac{8 - 15}{4})

Popular Examples

f(x)=sqrt((x^2-3x+2)/(x^2-3x))

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

y = sin^{2} (ln (x))

f(x)=5log_{10}(x+1)+10

f (x) = 5 lo g_{10} (x + 1) + 10

f(x)=-0.5x^2+30x-200

f (x) = - 0.5 x^{2} + 30 x - 200

f(t)={t:0<t<1,2t^2:t>= 1}

f (t) = {t : 0 < t < 1, 2 t^{2} : t \geq 1}

Frequently Asked Questions (FAQ)

What is the y=((x^2+x-12))/((x^2-4)) ?
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