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Popular >

y={sqrt(x^2-4):x<0,x^3-x:x>= 0}

Solution

y = {x^{2} - 4 : x < 0, x^{3} - x : x \geq 0}

Solution

Domain : x \leq - 2 or x \geq 0

X Intercepts : (- 2, 0), (0, 0), (1, 0), Y Intercepts : (0, 0)

Asymptotes : Slant y = - x

Monotone Intervals : Decreasing : - \infty < x < - 2, Decreasing : 0 < x < \frac{1}{3}, Increasing : \frac{1}{3} < x < \infty

+1

Interval Notation

Domain : (- \infty, - 2] \cup [0, \infty)

Solution steps

Domain of

{x^{2} - 4 : x < 0, x^{3} - x : x \geq 0} : x \leq - 2 or x \geq 0

Axis interception points of

{x^{2} - 4 : x < 0, x^{3} - x : x \geq 0} :

X Intercepts

: (- 2, 0), (0, 0), (1, 0),

Y Intercepts

: (0, 0)

Asymptotes of

{x^{2} - 4 : x < 0, x^{3} - x : x \geq 0} :

Slant

: y = - x

Monotone Intervals of

{x^{2} - 4 : x < 0, x^{3} - x : x \geq 0} :

Decreasing

: - \infty < x < - 2,

Decreasing

: 0 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Graph

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f (x) = x^{2} - 4 x + 6

f (x) = x^{2} - 2 x + 10

Frequently Asked Questions (FAQ)

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