Author Topic: Functions  (Read 1119 times)

Offline Kgatlhi

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Functions
« 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.

elemis

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Re: Functions
« Reply #1 on: October 09, 2010, 02:45:18 pm »
Une momento.

elemis

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Re: Functions
« Reply #2 on: October 09, 2010, 02:50:56 pm »
Is the range  1\le y \le5

Offline ashish

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Re: Functions
« Reply #3 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

Offline ashish

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Re: Functions
« Reply #4 on: October 09, 2010, 02:54:39 pm »
Is the range  1\le y \le5
lol
:D
yeah this is the answer

elemis

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Re: Functions
« Reply #5 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.

Offline ashish

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Re: Functions
« Reply #6 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

Offline Kgatlhi

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Re: Functions
« Reply #7 on: October 09, 2010, 03:59:07 pm »
thanks guys!  :)