Step by step
The question
Question: find f(−1) for f(x) = 4 if x < 2, x − 1 if x ≥ 2.
f(x) = 4 if x < 2
= x − 1 if x ≥ 2
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 second rule!
It is only for x greater than or equal to 2, and −1 is not.
Careful: not f(−1) = (−1) − 1 = −2 ✗
1 Find the right piece
Let's see where each rule works on a number line.
So we use this rule: 4.
2 Read the rule
This rule has no x.
It always gives 4.
So f(−1) = 4.
f(−1) = 4
3 Check
Let's check: does −1 fit each rule's x's?
Only one must say yes.
first rule: −1 < 2 yes
second rule: −1 ≥ 2 no ✗
Only the first rule fits.
So f(−1) is right!
Let's look back.
First: find the right piece.
Then: read the rule.
Last: check.
Answer
f(−1) = 4