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Popular >

y=(x^2-x+1)/(x^2+1)

Solution

y = \frac{x ^{2} - x + 1}{x ^{2} + 1}

Solution

Domain : - \infty < x < \infty

Range : \frac{1}{2} \leq f (x) \leq \frac{3}{2}

Y Intercepts : (0, 1)

Asymptotes : Horizontal y = 1

Extreme Points : Maximum (- 1, \frac{3}{2}), Minimum (1, \frac{1}{2})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{2}, \frac{3}{2}]

Solution steps

Domain of

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

Range of

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

Axis interception points of

\frac{x ^{2} - x + 1}{x ^{2} + 1} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{x ^{2} - x + 1}{x ^{2} + 1} :

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} - x + 1}{x ^{2} + 1} :

Maximum

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

Minimum

(1, \frac{1}{2})

Popular Examples

f(x)=(xcos(x)-sin(x))/(x^2)

f (x) = \frac{x cos ( x ) - sin ( x )}{x ^{2}}

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

f (x) = 12 - 5 x

y = \frac{1}{2} e^{- x}

f(x)=-2^{(-2+3x)}-4

f (x) = - 2^{(- 2 + 3 x)} - 4

Frequently Asked Questions (FAQ)

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