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Popular >

f(z)=(5z^2+3z)/(z^2+3)(-3)

Solution

f (z) = \frac{5 z ^{2} + 3 z}{z ^{2} + 3} (- 3)

Solution

Domain : - \infty < z < \infty

Range : - 37 - \frac{15}{2} \leq f (z) < - 15 or - 15 < f (z) \leq 37 - \frac{15}{2}

X Intercepts : (0, 0), (- \frac{3}{5}, 0), Y Intercepts : (0, 0)

Asymptotes : Horizontal y = - 15

Extreme Points : Maximum (5 - 27, - \frac{3 ( 5 - 2 7 )}{2}), Minimum (5 + 27, - \frac{3 ( 5 + 2 7 )}{2})

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Interval Notation

Domain : (- \infty, \infty)

Range : [- 37 - \frac{15}{2}, - 15) \cup (- 15, 37 - \frac{15}{2}]

Solution steps

Domain of

\frac{5 z ^{2} + 3 z}{z ^{2} + 3} (- 3) : - \infty < z < \infty

Range of

\frac{5 z ^{2} + 3 z}{z ^{2} + 3} (- 3) : - 37 - \frac{15}{2} \leq f (z) < - 15 or - 15 < f (z) \leq 37 - \frac{15}{2}

Axis interception points of

\frac{5 z ^{2} + 3 z}{z ^{2} + 3} (- 3) :

X Intercepts

: (0, 0), (- \frac{3}{5}, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{5 z ^{2} + 3 z}{z ^{2} + 3} (- 3) :

Horizontal

: y = - 15

Extreme Points of

\frac{5 z ^{2} + 3 z}{z ^{2} + 3} (- 3) :

Maximum

(5 - 27, - \frac{3 ( 5 - 2 7 )}{2}),

Minimum

(5 + 27, - \frac{3 ( 5 + 2 7 )}{2})

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Frequently Asked Questions (FAQ)

What is the f(z)=(5z^2+3z)/(z^2+3)(-3) ?
The f(z)=(5z^2+3z)/(z^2+3)(-3) is