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Popular >

f(x)=(3x^2-x-2)/(5x^2+4x+1)

Solution

f (x) = \frac{3 x ^{2} - x - 2}{5 x ^{2} + 4 x + 1}

Solution

Domain : - \infty < x < \infty

Range : - \frac{5}{2} - \frac{5}{2} \leq f (x) \leq \frac{5}{2} - \frac{5}{2}

X Intercepts : (1, 0), (- \frac{2}{3}, 0), Y Intercepts : (0, - 2)

Asymptotes : Horizontal y = \frac{3}{5}

Extreme Points : Maximum (- \frac{13 + 5 2}{17}, \frac{5 ( 2 - 1 )}{2}), Minimum (\frac{- 13 + 5 2}{17}, - \frac{5 ( 1 + 2 )}{2})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{5}{2} - \frac{5}{2}, \frac{5}{2} - \frac{5}{2}]

Solution steps

Domain of

\frac{3 x ^{2} - x - 2}{5 x ^{2} + 4 x + 1} : - \infty < x < \infty

Range of

\frac{3 x ^{2} - x - 2}{5 x ^{2} + 4 x + 1} : - \frac{5}{2} - \frac{5}{2} \leq f (x) \leq \frac{5}{2} - \frac{5}{2}

Axis interception points of

\frac{3 x ^{2} - x - 2}{5 x ^{2} + 4 x + 1} :

X Intercepts

: (1, 0), (- \frac{2}{3}, 0),

Y Intercepts

: (0, - 2)

Asymptotes of

\frac{3 x ^{2} - x - 2}{5 x ^{2} + 4 x + 1} :

Horizontal

: y = \frac{3}{5}

Extreme Points of

\frac{3 x ^{2} - x - 2}{5 x ^{2} + 4 x + 1} :

Maximum

(- \frac{13 + 5 2}{17}, \frac{5 ( 2 - 1 )}{2}),

Minimum

(\frac{- 13 + 5 2}{17}, - \frac{5 ( 1 + 2 )}{2})

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Frequently Asked Questions (FAQ)

What is the f(x)=(3x^2-x-2)/(5x^2+4x+1) ?
The f(x)=(3x^2-x-2)/(5x^2+4x+1) is