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Popular >

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

Solution

f (x) = 3 cos (\frac{π}{3} x + \frac{π}{2}) - 2

Solution

Period : 6

Domain : - \infty < x < \infty

Range : - 5 \leq f (x) \leq 1

X Intercepts : (\frac{9}{2} + \frac{3 arccos ( \frac{2}{3} )}{π} + 6 n, 0), (\frac{9}{2} - \frac{3 arccos ( \frac{2}{3} )}{π} + 6 n, 0), Y Intercepts : (0, - 2)

Asymptotes : None

Extreme Points : Minimum (\frac{3}{2} + 6 n, - 5), Maximum (\frac{9}{2} + 6 n, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 5, 1]

Solution steps

Periodicity of

3 cos (\frac{π}{3} x + \frac{π}{2}) - 2 : 6

Domain of

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

Range of

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

Axis interception points of

3 cos (\frac{π}{3} x + \frac{π}{2}) - 2 :

X Intercepts

: (\frac{9}{2} + \frac{3 arccos ( \frac{2}{3} )}{π} + 6 n, 0), (\frac{9}{2} - \frac{3 arccos ( \frac{2}{3} )}{π} + 6 n, 0),

Y Intercepts

: (0, - 2)

Asymptotes of

3 cos (\frac{π}{3} x + \frac{π}{2}) - 2 :

None

Extreme Points of

3 cos (\frac{π}{3} x + \frac{π}{2}) - 2 :

Minimum

(\frac{3}{2} + 6 n, - 5),

Maximum

(\frac{9}{2} + 6 n, 1)

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Frequently Asked Questions (FAQ)

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