Question

QUESTIONS HELP ME PLEASE.....

Answer 1

NOTES:

y = sin x

x | y

-2π | 0

`-(3\pi)/(2)` | 1

-π | 0

`-(\pi)/(2)` | -1

0 | 0

`(\pi)/(2)` | 1

π | 0

`(3\pi)/(2)` | -1

2π | 0

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

Graph: B

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

1) NO

Even function is when f(x) = f(-x)

Check: sin (x) = sin (-x)

Let x =
`(\pi)/(2)`

sin (
`(\pi)/(2)`) = 1

sin (
`-(\pi)/(2)`) = -1

f(x) ≠ f(-x) so sin (x) is not an even function

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

2) YES

sin (-2π) = 0

sin (
`-(3\pi)/(2)`) = 1

0 → 1 is "increasing"

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

3) YES

There are no restrictions on x so the domain is x = All Real Numbers

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

4) YES

y = sin (x) has the coordinate (0, 0) so the y-intercept is 0

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

5) NO

Let n = 0, then
`(2(0) + 1)/(2)\pi`

=
`(\pi)/(2)`

sin (
`(\pi)/(2)`) = 1 so it is not a zero

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

6) NO

Let n = 0, then x = 0π

= 0

This is a zero, not a minimum. Minimums are when y = -1.