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Popular >

y=-3sin(2x+pi)+1/2

Solution

y = - 3 sin (2 x + π) + \frac{1}{2}

Solution

Period : π

Domain : - \infty < x < \infty

Range : - \frac{5}{2} \leq f (x) \leq \frac{7}{2}

X Intercepts : (\frac{π}{2} + \frac{arcsin ( \frac{1}{6} )}{2} + πn, 0), (- \frac{arcsin ( \frac{1}{6} )}{2} + π + πn, 0), Y Intercepts : (0, \frac{1}{2})

Asymptotes : None

Extreme Points : Maximum (\frac{π}{4} + πn, \frac{7}{2}), Minimum (\frac{3 π}{4} + πn, - \frac{5}{2})

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Solution steps

Periodicity of

- 3 sin (2 x + π) + \frac{1}{2} : π

Domain of

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

Range of

- 3 sin (2 x + π) + \frac{1}{2} : - \frac{5}{2} \leq f (x) \leq \frac{7}{2}

Axis interception points of

- 3 sin (2 x + π) + \frac{1}{2} :

X Intercepts

: (\frac{π}{2} + \frac{arcsin ( \frac{1}{6} )}{2} + πn, 0), (- \frac{arcsin ( \frac{1}{6} )}{2} + π + πn, 0),

Y Intercepts

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

Asymptotes of

- 3 sin (2 x + π) + \frac{1}{2} :

None

Extreme Points of

- 3 sin (2 x + π) + \frac{1}{2} :

Maximum

(\frac{π}{4} + πn, \frac{7}{2}),

Minimum

(\frac{3 π}{4} + πn, - \frac{5}{2})

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