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

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f(x)=sqrt(x^2+x+2)

f (x) = x^{2} + x + 2

Domain : - \infty < x < \infty

Range : f (x) \geq \frac{7}{2}

Y Intercepts : (0, 2)

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

Extreme Points : Minimum (- \frac{1}{2}, \frac{7}{2})

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{7}{2}, \infty)

Solution steps

Domain of

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

Range of

x^{2} + x + 2 : f (x) \geq \frac{7}{2}

Axis interception points of

x^{2} + x + 2 :

Y Intercepts

: (0, 2)

Asymptotes of

x^{2} + x + 2 :

Slant

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

Extreme Points of

x^{2} + x + 2 :

Minimum

(- \frac{1}{2}, \frac{7}{2})

f (θ) = \frac{1 + sin ( θ ) + cos ( θ )}{1 + sin ( θ ) - cos ( θ )}

f (x) = x^{4} - 7 x + 8

y = 3 \cdot (\frac{3}{5})^{x + 2} - 4

p (x) = - x^{2} + 100

f (x) = - 2 x^{2} - 20 x - 47