Step by step
The question
Question: find f(5) for f(x) = x − 3 if x ≤ 1, 2x if x > 1.
f(x) = x − 3 if x ≤ 1
= 2x if x > 1
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 or equal to 1, and 5 is not.
Careful: not f(5) = 5 − 3 = 2 ✗
1 Find the right piece
Let's see where each rule works on a number line.
So we use this rule: 2x.
2 Put 5 in
Put 5 in place of x in 2x.
We write it in brackets.
f(5) = 2(5)
2(5) = 2 × 5
2(5) means 2 times 5.
2 times 5 is 10.
f(5) = 10
So f(5) = 10.
3 Check
Let's check: does 5 fit each rule's x's?
Only one must say yes.
first rule: 5 ≤ 1 no ✗
second rule: 5 > 1 yes
Only the second rule fits.
So f(5) is right!
Let's look back.
First: find the right piece.
Then: put 5 in.
Last: check.
Answer
f(5) = 10