Piecewise Function: Find Expression for Graph | Homework Help

AI Thread Summary
The discussion centers on determining the correct expressions for a piecewise function based on a given graph. The first segment of the function is defined as y = -x + 3 for the interval [0, 3], while the second segment is y = 2x - 6 for the interval (3, 5). There is confusion regarding the use of brackets versus parentheses at x = 3, as both functions yield the same y-value of 0 at that point. It is clarified that either notation can be valid, as long as the chosen intervals are consistent with the function definitions. Ultimately, the choice of interval notation does not affect the validity of the piecewise function.
Rijad Hadzic
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Homework Statement


Hello I uploaded a picture of the image.

Find an expression for a function who's graph is the given curve.

Homework Equations

The Attempt at a Solution


The first function [0,3] y= -x+3 and the second one is y=2x-6 from 3 to 5

what I don't get, is why isn't the second one [3,5], instead the answer is (3,5)..

The way I see it at that point, x=3, it can be anyone of those equations...
 

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My thinking is because the function goes from right to left it would make sense that the first function is less than or equal to 3 but I'm not sure if that's right..
 
Rijad Hadzic said:

Homework Statement


Hello I uploaded a picture of the image.

Find an expression for a function who's graph is the given curve.

Homework Equations

The Attempt at a Solution


The first function [0,3] y= -x+3 and the second one is y=2x-6 from 3 to 5

what I don't get, is why isn't the second one [3,5], instead the answer is (3,5)..

The way I see it at that point, x=3, it can be anyone of those equations...
And that's why you should choose which function goes with which interval. If ##x \in [0. 3]## you use the formula y = -x + 3. If ##x \in (3, 5)##, you use the formula y = 2x - 6.
 
Mark44 said:
And that's why you should choose which function goes with which interval. If ##x \in [0. 3]## you use the formula y = -x + 3. If ##x \in (3, 5)##, you use the formula y = 2x - 6.

So the reason my books answer was [0,3] for y=-x + 3 was because they chose it to be that.

But if I wanted to I could choose [0,3) for y=-x+3 and [3,5] for 2x - 6 and my answer would still be valid because that's what I decided to choose?
 
Rijad Hadzic said:
So the reason my books answer was [0,3] for y=-x + 3 was because they chose it to be that.

But if I wanted to I could choose [0,3) for y=-x+3 and [3,5] for 2x - 6 and my answer would still be valid because that's what I decided to choose?
Yes. At x = 3, both functions have y-values of 0, so it doesn't matter how you define the endpoints of the two intervals.
 

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