What is the y=(z^2+1)/(z^2-1) ?

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y=(z^2+1)/(z^2-1)

y = \frac{z ^{2} + 1}{z ^{2} - 1}

Domain : z < - 1 or - 1 < z < 1 or z > 1

Range : f (z) \leq - 1 or f (z) > 1

Y Intercepts : (0, - 1)

Asymptotes : Vertical z = - 1, z = 1, Horizontal y = 1

Extreme Points : Maximum (0, - 1)

Interval Notation

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

Range : (- \infty, - 1] \cup (1, \infty)

Solution steps

Domain of

\frac{z ^{2} + 1}{z ^{2} - 1} : z < - 1 or - 1 < z < 1 or z > 1

Range of

\frac{z ^{2} + 1}{z ^{2} - 1} : f (z) \leq - 1 or f (z) > 1

Axis interception points of

\frac{z ^{2} + 1}{z ^{2} - 1} :

Y Intercepts

: (0, - 1)

Asymptotes of

\frac{z ^{2} + 1}{z ^{2} - 1} :

Vertical

: z = - 1, z = 1,

Horizontal

: y = 1

Extreme Points of

\frac{z ^{2} + 1}{z ^{2} - 1} :

Maximum

(0, - 1)

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