What is the f(x)=(3x^2-8x-3)/(2x^2+7x-4) ?

The f(x)=(3x^2-8x-3)/(2x^2+7x-4) is

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f(x)=(3x^2-8x-3)/(2x^2+7x-4)

f (x) = \frac{3 x ^{2} - 8 x - 3}{2 x ^{2} + 7 x - 4}

Domain : x < - 4 or - 4 < x < \frac{1}{2} or x > \frac{1}{2}

Range : - \infty < f (x) < \infty

X Intercepts : (3, 0), (- \frac{1}{3}, 0), Y Intercepts : (0, \frac{3}{4})

Asymptotes : Vertical x = - 4, x = \frac{1}{2}, Horizontal y = \frac{3}{2}

Extreme Points : None

Interval Notation

Domain : (- \infty, - 4) \cup (- 4, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

\frac{3 x ^{2} - 8 x - 3}{2 x ^{2} + 7 x - 4} : x < - 4 or - 4 < x < \frac{1}{2} or x > \frac{1}{2}

Range of

\frac{3 x ^{2} - 8 x - 3}{2 x ^{2} + 7 x - 4} : - \infty < f (x) < \infty

Axis interception points of

\frac{3 x ^{2} - 8 x - 3}{2 x ^{2} + 7 x - 4} :

X Intercepts

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

Y Intercepts

: (0, \frac{3}{4})

Asymptotes of

\frac{3 x ^{2} - 8 x - 3}{2 x ^{2} + 7 x - 4} :

Vertical

: x = - 4, x = \frac{1}{2},

Horizontal

: y = \frac{3}{2}

Extreme Points of

\frac{3 x ^{2} - 8 x - 3}{2 x ^{2} + 7 x - 4} :

None

f (x) = 8^{x + 3}

f (x) = \frac{x ^{3}}{4} - 3 x

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

f (y) = y^{9}

y = 3 x + 30