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Popular >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : - \frac{1}{2} + \frac{5}{2} \leq f (x) \leq \frac{1}{2} + \frac{5}{2}

Y Intercepts : (0, 3)

Asymptotes : Horizontal y = 2

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{2} + \frac{5}{2}, \frac{1}{2} + \frac{5}{2}]

Solution steps

Domain of

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

Range of

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

Axis interception points of

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

Y Intercepts

: (0, 3)

Asymptotes of

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

Horizontal

: y = 2

Extreme Points of

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

Maximum

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

Minimum

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

Popular Examples

f(x)=-x^3+2x^2+3x-1

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

y = x - 5 + 4

v(x)=-0.1*x^2+1.6*x+2.7

v (x) = - 0.1 \cdot x^{2} + 1.6 \cdot x + 2.7

y = 2 + x + 1

y = sin (x - 1)

Frequently Asked Questions (FAQ)

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