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Popular >

f(x)=2cos(3x+pi)-1

Solution

f (x) = 2 cos (3 x + π) - 1

Solution

Period : \frac{2 π}{3}

Domain : - \infty < x < \infty

Range : - 3 \leq f (x) \leq 1

X Intercepts : (\frac{4 π}{9} + \frac{2 πn}{3}, 0), (\frac{2 π}{9} + \frac{2 πn}{3}, 0), Y Intercepts : (0, - 3)

Asymptotes : None

Extreme Points : Minimum (\frac{2 π}{3} n, - 3), Maximum (\frac{π}{3} + \frac{2 π}{3} n, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 3, 1]

Solution steps

Periodicity of

2 cos (3 x + π) - 1 : \frac{2 π}{3}

Domain of

2 cos (3 x + π) - 1 : - \infty < x < \infty

Range of

2 cos (3 x + π) - 1 : - 3 \leq f (x) \leq 1

Axis interception points of

2 cos (3 x + π) - 1 :

X Intercepts

: (\frac{4 π}{9} + \frac{2 πn}{3}, 0), (\frac{2 π}{9} + \frac{2 πn}{3}, 0),

Y Intercepts

: (0, - 3)

Asymptotes of

2 cos (3 x + π) - 1 :

None

Extreme Points of

2 cos (3 x + π) - 1 :

Minimum

(\frac{2 π}{3} n, - 3),

Maximum

(\frac{π}{3} + \frac{2 π}{3} n, 1)

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Frequently Asked Questions (FAQ)

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