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Mathematics, 22.03.2021 23:40 lrasanaoaksandfurana

Let’s practice making the decision of which part of the piecewise function to substitute our x value into, and then evaluating. f(x)=⎧⎩⎨βŽͺβŽͺβˆ’6,xβ‰€βˆ’13,βˆ’1
For the above piecewise function, find f(x) for the following.

x=βˆ’3
This one is pretty straightforward. If x=βˆ’3, which domain category does it fit into?

Answer

Find f(βˆ’3):

Since βˆ’3β‰€βˆ’1, we know that the answer to f(βˆ’3) will be βˆ’6, since that is the part of the function that matches with xβ‰€βˆ’1. When you have just a constant for a part of a piecewise function, that means that any input (x-value), you put in that falls within that domain (in this case all numbers less than or equal to βˆ’1), you will always get the answer βˆ’6. You don’t even have to substitute and calculate anything. That means that f(βˆ’3)=βˆ’6 and f(βˆ’4)=βˆ’6, and so on.

x=βˆ’1
Careful, this one can be a little bit tricky. Look carefully at those inequality signs. Which domain does this x=βˆ’1 fit into?

Answer
x≀-1

Find f(βˆ’1)

If you look at your domain categories, you may have noticed that βˆ’1 is listed twice. How do you decide which one is the right one? Notice that for xβˆ’1, this is saying x is less than or equal to βˆ’1, so this is the category that applies. The other, βˆ’1
x=2
Which domain does this x=2 fit into?

Answer
-1 < x < 3

Find f(2).

f(2)= Answer

x=3
Which domain does this x=3 fit into? (Be extra careful with this one again, remember.)

Answer
xβ‰₯3

Find f(3). (Hint: You will need to actually substitute and calculate for this one.)

f(3)= Answer

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Let’s practice making the decision of which part of the piecewise function to substitute our x value...
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