Question

QUESTIONS HELP ME PLEASE...

Answer 1

y = A sin (Bx)

Period: starts at 0 and restarts at 4π

Period = 4π

Period =
`(2\pi)/(B)`

4π =
`(2\pi)/(B)`

B =
`(2\pi)/(4\pi)`

B =
`(1)/(2)`

A = amplitude. The minimum is -3 and the maximum is +3.

A =
`(3 - (-3))/(2)`

A =
`(6)/(2)`

A = 3

y = A sin (Bx)

↓ ↓

y = 3 sin (
`(1)/(2)x`)

*******************************************************

sin is an odd function so f(x) = -f(x)

Answer: y =
`-(1)/(2)` (sin 2πx)

form is: y = A sin (Bx) ; where A is the amplitude so,

Amplitude (A) = (
`(1)/(2)`)

The range is between -1/2 and +1/2 so,

Range = [
`-(1)/(2)` ,
`(1)/(2)`]

Period =
`(2\pi)/(B)`

Period =
`(2\pi)/(|-2\pi|)`

Period = 1

y =
`(1)/(2)` sin (-2πx)

x=0 ⇒ y =
`(1)/(2)` sin(-2π(0))

=
`(1)/(2)` sin(0)

=
`(1)/(2)` (0)

= 0

(0, 0) works!

x=
`(\pi)/(2)` ⇒ y =
`(1)/(2)` sin(-2π(
`(\pi)/(2)`))

=
`(1)/(2)` sin(-π²)

=
`(1)/(2)` (0.17)

= 0.085

(
`(\pi)/(2)`, 1) does NOT work

see attachment for the rest of the points:

(π, 0) does NOT work

`((3\pi)/(2), -1)` does NOT work

(2π, 0) does NOT work

Graph: D