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Popular >

F(z)=(4z)/((z-3)(z-1))

Solution

F (z) = \frac{4 z}{( z - 3 ) ( z - 1 )}

Solution

Domain : z < 1 or 1 < z < 3 or z > 3

Range : f (z) \leq - 23 - 4 or f (z) \geq 23 - 4

X Intercepts : (0, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical z = 1, z = 3, Horizontal y = 0

Extreme Points : Minimum (- 3, 2 (3 - 2)), Maximum (3, - 2 (3 + 2))

+1

Interval Notation

Domain : (- \infty, 1) \cup (1, 3) \cup (3, \infty)

Range : (- \infty, - 23 - 4] \cup [23 - 4, \infty)

Solution steps

Domain of

\frac{4 z}{( z - 3 ) ( z - 1 )} : z < 1 or 1 < z < 3 or z > 3

Range of

\frac{4 z}{( z - 3 ) ( z - 1 )} : f (z) \leq - 23 - 4 or f (z) \geq 23 - 4

Axis interception points of

\frac{4 z}{( z - 3 ) ( z - 1 )} :

X Intercepts

: (0, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{4 z}{( z - 3 ) ( z - 1 )} :

Vertical

: z = 1, z = 3,

Horizontal

: y = 0

Extreme Points of

\frac{4 z}{( z - 3 ) ( z - 1 )} :

Minimum

(- 3, 2 (3 - 2)),

Maximum

(3, - 2 (3 + 2))

Popular Examples

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f (x) = x^{3} - 8 x^{2} - 23 x + 30

f(x)=7cos^2(x)+2

f (x) = 7 cos^{2} (x) + 2

f(x)=sqrt(x^2+2x-3)

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

f(t)=e^{-2t}(3-cos(t)+t^3)

f (t) = e^{- 2 t} (3 - cos (t) + t^{3})

f (x) = x + (\frac{1}{x})

Frequently Asked Questions (FAQ)

What is the F(z)=(4z)/((z-3)(z-1)) ?
The F(z)=(4z)/((z-3)(z-1)) is