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Popular >

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

Solution

f (x) = - 2 sin (\frac{1}{2} x - \frac{π}{3}) + 1

Solution

Period : 4 π

Domain : - \infty < x < \infty

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

X Intercepts : (π + 4 πn, 0), (\frac{7 π}{3} + 4 πn, 0), Y Intercepts : (0, 3 + 1)

Asymptotes : None

Extreme Points : Minimum (\frac{5 π}{3} + 4 πn, - 1), Maximum (\frac{11 π}{3} + 4 πn, 3)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 3]

Solution steps

Periodicity of

- 2 sin (\frac{1}{2} x - \frac{π}{3}) + 1 : 4 π

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

: (π + 4 πn, 0), (\frac{7 π}{3} + 4 πn, 0),

Y Intercepts

: (0, 3 + 1)

Asymptotes of

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

None

Extreme Points of

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

Minimum

(\frac{5 π}{3} + 4 πn, - 1),

Maximum

(\frac{11 π}{3} + 4 πn, 3)

Popular Examples

f (x) = x^{2} - 5 x - 36

f (x) = x^{2} - 5 x + 15

y = 3 cos (x + \frac{π}{3})

g (x) = - x

f(x)=2x^4+5x^3-11x^2-204x+12

f (x) = 2 x^{4} + 5 x^{3} - 11 x^{2} - 204 x + 12

Frequently Asked Questions (FAQ)

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