Step by step
The question
Question: find f(3) for f(x) = 2x if x < 0, x + 5 if x ≥ 0.
f(x) = 2x if x < 0
= x + 5 if x ≥ 0
This is a piecewise function.
It has 2 rules.
Which rule we use depends on x.
Each x uses only one rule.
piecewise: a different rule for different x's
each x uses only one rule
Careful!
Not the first rule!
It is only for x less than 0, and 3 is not.
Careful: not f(3) = 2(3) = 6 ✗
1 Find the right piece
Let's see where each rule works on a number line.
So we use this rule: x + 5.
2 Put 3 in
Put 3 in place of x in x + 5.
f(3) = 3 + 5
3 plus 5 is 8.
f(3) = 8
So f(3) = 8.
3 Check
Let's check: does 3 fit each rule's x's?
Only one must say yes.
first rule: 3 < 0 no ✗
second rule: 3 ≥ 0 yes
Only the second rule fits.
So f(3) is right!
Let's look back.
First: find the right piece.
Then: put 3 in.
Last: check.
Answer
f(3) = 8