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

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

Answer

Find f(−3):

Since −3≤−1, we know that the answer to f(−3) will be −6, since that is the part of the function that matches with x≤−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 −1), you will always get the answer −6. You don’t even have to substitute and calculate anything. That means that f(−3)=−6 and f(−4)=−6, and so on.

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

Answer
x≤-1

Find f(−1)

If you look at your domain categories, you may have noticed that −1 is listed twice. How do you decide which one is the right one? Notice that for x−1, this is saying x is less than or equal to −1, so this is the category that applies. The other, −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
x≥3

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

f(3)= Answer