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)=⎧⎩⎨⎪⎪−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
Answers: 3
Mathematics, 21.06.2019 16:00, dtovar4922
Apatient is to take 60 mg of an antibiotic on day 1, take 45mg on days 2 and 3, take 30mg on days 4 and 5 and take 15 mg on days 6 and 7. how many total mg will the patient take?
Answers: 1
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