What is the y=sqrt(x^2+x+1) ?

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y=sqrt(x^2+x+1)

y = x^{2} + x + 1

Domain : - \infty < x < \infty

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

Y Intercepts : (0, 1)

Asymptotes : Slant y = x + \frac{1}{2}, y = - x - \frac{1}{2}

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

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{3}{2}, \infty)

Solution steps

Domain of

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

Range of

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

Axis interception points of

x^{2} + x + 1 :

Y Intercepts

: (0, 1)

Asymptotes of

x^{2} + x + 1 :

Slant

: y = x + \frac{1}{2}, y = - x - \frac{1}{2}

Extreme Points of

x^{2} + x + 1 :

Minimum

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

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