For the function

_____{x+3 if -5≤x<2

f(x)={x^2 if 2≤x≤4

I have to sketch the graph, determine the domain and range of f(x), and determine f(2). Help please? (Headbang)

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- Sep 21st 2009, 07:09 AMBeSweeetPiecewise Function - Domain & Range
For the function

_____{x+3 if -5≤x<2

f(x)={x^2 if 2≤x≤4

I have to sketch the graph, determine the domain and range of f(x), and determine f(2). Help please? (Headbang) - Sep 21st 2009, 07:22 AMred_dog

The domain is .

To find the range we can use the following statement abou function:

If and are two subsets of A, then

In this case let

We have .

Then the range is - Sep 21st 2009, 07:34 AMBeSweeet
- Sep 21st 2009, 07:47 AMred_dog
- Sep 21st 2009, 08:08 AMstapel
Sketch y = x + 3, and then erase everything before x = -5 and after x = 2. Make sure to draw a filled-in circle for the left-hand endpoint and an "open" circle for the right-hand endpoint.

Then sketch y = x^2, and erase everything before x = 2 and after x = 4. Make sure to draw filled-in circles for each of the endpoints.

The domain is given: it's the x-values for which the function is defined.

To find the range, look at your graph. Which y-values are covered by this graph? (If you "collapsed the graph sideways onto the y-axis, which portions would be covered?)

The function is defined for x = 2. So look at the function rule, find the half which is defined for x = 2, and plug 2 in for x in that half's rule.

(Wink) - Sep 21st 2009, 02:11 PMBeSweeet
- Sep 21st 2009, 02:35 PMstapel
- Sep 21st 2009, 02:53 PMBeSweeet