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Popular >

y=-3sin(1/2 x)

Solution

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

Solution

Period : 4 π

Domain : - \infty < x < \infty

Range : - 3 \leq f (x) \leq 3

X Intercepts : (4 πn, 0), (2 π + 4 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (π + 4 πn, - 3), Maximum (3 π + 4 πn, 3)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 3, 3]

Solution steps

Periodicity of

- 3 sin (\frac{1}{2} x) : 4 π

Domain of

- 3 sin (\frac{1}{2} x) : - \infty < x < \infty

Range of

- 3 sin (\frac{1}{2} x) : - 3 \leq f (x) \leq 3

Axis interception points of

- 3 sin (\frac{1}{2} x) :

X Intercepts

: (4 πn, 0), (2 π + 4 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

- 3 sin (\frac{1}{2} x) :

None

Extreme Points of

- 3 sin (\frac{1}{2} x) :

Minimum

(π + 4 πn, - 3),

Maximum

(3 π + 4 πn, 3)

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f(x)=x^2-12x+144

f (x) = x^{2} - 12 x + 144

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