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Popular >

f(x)=-7cos(1/2 x+pi/6)+5

Solution

f (x) = - 7 cos (\frac{1}{2} x + \frac{π}{6}) + 5

Solution

Period : 4 π

Domain : - \infty < x < \infty

Range : - 2 \leq f (x) \leq 12

X Intercepts : (2 arccos (\frac{5}{7}) - \frac{π}{3} + 4 πn, 0), (4 π - 2 arccos (\frac{5}{7}) - \frac{π}{3} + 4 πn, 0), Y Intercepts : (0, - \frac{7 3}{2} + 5)

Asymptotes : None

Extreme Points : Maximum (\frac{5 π}{3} + 4 πn, 12), Minimum (\frac{11 π}{3} + 4 πn, - 2)

+1

Solution steps

Periodicity of

- 7 cos (\frac{1}{2} x + \frac{π}{6}) + 5 : 4 π

Domain of

- 7 cos (\frac{1}{2} x + \frac{π}{6}) + 5 : - \infty < x < \infty

Range of

- 7 cos (\frac{1}{2} x + \frac{π}{6}) + 5 : - 2 \leq f (x) \leq 12

Axis interception points of

- 7 cos (\frac{1}{2} x + \frac{π}{6}) + 5 :

X Intercepts

: (2 arccos (\frac{5}{7}) - \frac{π}{3} + 4 πn, 0), (4 π - 2 arccos (\frac{5}{7}) - \frac{π}{3} + 4 πn, 0),

Y Intercepts

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

Asymptotes of

- 7 cos (\frac{1}{2} x + \frac{π}{6}) + 5 :

None

Extreme Points of

- 7 cos (\frac{1}{2} x + \frac{π}{6}) + 5 :

Maximum

(\frac{5 π}{3} + 4 πn, 12),

Minimum

(\frac{11 π}{3} + 4 πn, - 2)

Popular Examples

y = 4 sin (5 x) - 3

f(x)=(x^2-12)/(x+4)

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f (x) = - 2 x^{6} + 6 x^{5} + 18 x^{4} - 54 x^{3}

f (x) = - 2 + 1

y = 3 x^{5} - 10 x^{3}

Frequently Asked Questions (FAQ)

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