What is the f(x)=(x^2-5x-24)/(x^2-7x-30) ?

The f(x)=(x^2-5x-24)/(x^2-7x-30) is

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f(x)=(x^2-5x-24)/(x^2-7x-30)

f (x) = \frac{x ^{2} - 5 x - 24}{x ^{2} - 7 x - 30}

Domain : x < - 3 or - 3 < x < 10 or x > 10

Range : f (x) < \frac{11}{13} or \frac{11}{13} < f (x) < 1 or f (x) > 1

X Intercepts : (8, 0), Y Intercepts : (0, \frac{4}{5})

Asymptotes : Vertical x = 10, Horizontal y = 1

Extreme Points : None

Interval Notation

Domain : (- \infty, - 3) \cup (- 3, 10) \cup (10, \infty)

Range : (- \infty, \frac{11}{13}) \cup (\frac{11}{13}, 1) \cup (1, \infty)

Solution steps

Domain of

\frac{x ^{2} - 5 x - 24}{x ^{2} - 7 x - 30} : x < - 3 or - 3 < x < 10 or x > 10

Range of

\frac{x ^{2} - 5 x - 24}{x ^{2} - 7 x - 30} : f (x) < \frac{11}{13} or \frac{11}{13} < f (x) < 1 or f (x) > 1

Axis interception points of

\frac{x ^{2} - 5 x - 24}{x ^{2} - 7 x - 30} :

X Intercepts

: (8, 0),

Y Intercepts

: (0, \frac{4}{5})

Asymptotes of

\frac{x ^{2} - 5 x - 24}{x ^{2} - 7 x - 30} :

Vertical

: x = 10,

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} - 5 x - 24}{x ^{2} - 7 x - 30} :

None

y = x e^{(- x)}

P (t) = - 6 t^{2} + 120 t + 600

y = 5 lo g_{3} (- x) - 5

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

f (x) = (2 x)^{2} - 1