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Popular >

g(x)=|x-2|+|x|-|x-1|

Solution

g (x) = ∣ x - 2 ∣ + ∣ x ∣ - ∣ x - 1 ∣

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 1

Y Intercepts : (0, 1)

Asymptotes : Slant y = x - 1

Extreme Points : Minimum (0, 1), Maximum (1, 2), Minimum (2, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [1, \infty)

Solution steps

Domain of

∣ x - 2 ∣ + ∣ x ∣ - ∣ x - 1 ∣ : - \infty < x < \infty

Range of

∣ x - 2 ∣ + ∣ x ∣ - ∣ x - 1 ∣ : f (x) \geq 1

Axis interception points of

∣ x - 2 ∣ + ∣ x ∣ - ∣ x - 1 ∣ :

Y Intercepts

: (0, 1)

Asymptotes of

∣ x - 2 ∣ + ∣ x ∣ - ∣ x - 1 ∣ :

Slant

: y = x - 1

Extreme Points of

∣ x - 2 ∣ + ∣ x ∣ - ∣ x - 1 ∣ :

Minimum

(0, 1),

Maximum

(1, 2),

Minimum

(2, 1)

Popular Examples

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f (x) = x^{3} - 4 x^{2} + 5 x - 1

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f(x)=2x+log_{33}(x)

f (x) = 2 x + lo g_{33} (x)

f(p)=(10p+13)^3

f (p) = (10 p + 13)^{3}

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f (x) = (sin (0.62 x))^{\frac{1}{2}}

Frequently Asked Questions (FAQ)

What is the g(x)=|x-2|+|x|-|x-1| ?
The g(x)=|x-2|+|x|-|x-1| is