IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Kgatlhi on October 09, 2010, 02:31:45 pm

Title: Functions
Post by: Kgatlhi on October 09, 2010, 02:31:45 pm: 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.
Title: Re: Functions
Post by: elemis on October 09, 2010, 02:45:18 pm: Une momento.
Title: Re: Functions
Post by: elemis on October 09, 2010, 02:50:56 pm: Is the range $1\le y \le5$
Title: Re: Functions
Post by: ashish on October 09, 2010, 02:51:08 pm: 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
Title: Re: Functions
Post by: ashish on October 09, 2010, 02:54:39 pm: Quote from: Ari Ben Canaan on October 09, 2010, 02:50:56 pm
Is the range $1\le y \le5$
lol
:D
yeah this is the answer
Title: Re: Functions
Post by: elemis on October 09, 2010, 02:58:50 pm: 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.
Title: Re: Functions
Post by: ashish on October 09, 2010, 03:01:57 pm: 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
Title: Re: Functions
Post by: Kgatlhi on October 09, 2010, 03:59:07 pm: thanks guys! :)