Functions

[Kgatlhi]

please help!

a function is defined by f(x)= 3- 2Sinx for 0<x<360 degrees (NB. the symbols should indicate that x is greater than or equal to and that x is less than or equal to respectively)

1. find the range of f

I've been taught to substitute the domain in the eq to get the answer but thats not working here.

[elemis]

Une momento.

[elemis]

Is the range 

[ashish]

y = 3-2sinx

sin 90 is 1
Y=3-2
 =1

sin270 is -1
Y=3-2(-1)
y=5

Y greater or equal to 1 or y less or equal to 5

[ashish]

Is the range 

lol

yeah this is the answer

[elemis]

I basically sketched the graph. The steps are as follows :

y = 3- 2sin x

First I drew the regular sine graph.

The part in blue represents a vertical stretch of -2. So I multiplied each Y Coordinate by -2

The part in red represents a vertical TRANSLATION of 3 units UPWARDS. So I added 3 to each Y COORDINATE.

You should get a graph as below :

Next, we look at the maximum and minimum Y Value : this is our range for the function.

[ashish]

yeah that's good but it's good to know that sin90 and sin270 are 1 and -1 (maximum and minimum) so as not loose time in exams

[Kgatlhi]

thanks guys!