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Popular >

f(x)=(|x+1|-3)/(1+|x-3|)

Solution

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

Solution

Domain : - \infty < x < \infty

Range : - \frac{3}{5} \leq f (x) \leq 1

X Intercepts : (- 4, 0), (2, 0), Y Intercepts : (0, - \frac{1}{2})

Asymptotes : Horizontal y = 1

Extreme Points : Minimum (- 1, - \frac{3}{5})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{3}{5}, 1]

Solution steps

Domain of

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

Range of

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

Axis interception points of

\frac{∣ x + 1 ∣ - 3}{1 + ∣ x - 3 ∣} :

X Intercepts

: (- 4, 0), (2, 0),

Y Intercepts

: (0, - \frac{1}{2})

Asymptotes of

\frac{∣ x + 1 ∣ - 3}{1 + ∣ x - 3 ∣} :

Horizontal

: y = 1

Extreme Points of

\frac{∣ x + 1 ∣ - 3}{1 + ∣ x - 3 ∣} :

Minimum

(- 1, - \frac{3}{5})

Popular Examples

f(x)=\sqrt[4]{x^2+x}

derivative of-3cos(2x+pi/3+2)

\frac{d}{d x} (- 3 cos (2 x + \frac{π}{3}) + 2)

y=(log_{5}(x))+2

y = (lo g_{5} (x)) + 2

f(n)=log_{2}(log_{2}(n))

f (n) = lo g_{2} (lo g_{2} (n))

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

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

Frequently Asked Questions (FAQ)

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