Worked examples
The question
Question: find f(4) for f(x) = 3x + 2.
f(x) = 3x + 2
f(x) is read "f of x".
It is a rule, called a function.
A number goes in for x.
The rule gives one answer out.
f(x) = "f of x"
x goes in → an answer comes out
1 Put the number in
f(4) means: put 4 in place of every x.
We write it in brackets.
f(4) = 3(4) + 2
2 Times and divide
Times comes before plus.
Order: ( ) → x² √ → × ÷ → + −
3(4) = 3 × 4
3(4) means 3 times 4.
3 times 4 is 12.
= 12 + 2
3 Plus and minus
12 plus 2 is 14.
f(4) = 14
So f(4) = 14.
Let's look back.
First: put the number in.
Then: times and divide.
Last: plus and minus.
▶ Watch it solved
The question
Question: find f(−2) for f(x) = 2x² − 3x + 1.
f(x) = 2x2 − 3x + 1
f(x) is read "f of x".
It is a rule, called a function.
A number goes in for x.
The rule gives one answer out.
f(x) = "f of x"
x goes in → an answer comes out
1 Put the number in
f(−2) means: put −2 in place of every x.
We write it in brackets.
The brackets keep the minus with the number.
f(−2) = 2(−2)2 − 3(−2) + 1
2 Powers
Powers come before times, minus and plus.
Order: ( ) → x² √ → × ÷ → + −
(−2)² means −2 times −2.
Minus times minus is plus.
(−2)2 = (−2) × (−2) = 4
That is 4.
= 2(4) − 3(−2) + 1
3 Times and divide
Times comes before minus and plus.
Times and divide: we go from left to right.
same kind: left → right
2(4) = 2 × 4
2(4) means 2 times 4.
2 times 4 is 8.
= 8 − 3(−2) + 1
Times comes before minus and plus.
3(−2) = 3 × (−2)
+ × − = −
3(−2) means 3 times −2.
Plus times minus is minus.
3 times 2 is 6.
So we get −6.
= 8 − (−6) + 1
4 Plus and minus
Plus and minus: we go from left to right.
Taking away a negative is the same as adding.
same kind: left → right
− (−) = +
So 8 − (−6) becomes 8 + 6.
= 8 + 6 + 1
8 plus 6 is 14.
= 14 + 1
14 plus 1 is 15.
f(−2) = 15
So f(−2) = 15.
Let's look back.
First: put the number in.
Then: powers.
Then: times and divide.
Last: plus and minus.
▶ Watch it solved
The question
Question: find f(−2) for f(x) = x³ − 2x.
f(x) = x3 − 2x
f(x) is read "f of x".
It is a rule, called a function.
A number goes in for x.
The rule gives one answer out.
f(x) = "f of x"
x goes in → an answer comes out
1 Put the number in
f(−2) means: put −2 in place of every x.
We write it in brackets.
The brackets keep the minus with the number.
f(−2) = (−2)3 − 2(−2)
2 Powers
Powers come before minus and times.
Order: ( ) → x² √ → × ÷ → + −
(−2)³ means −2 times −2 times −2.
An odd number of minuses gives minus.
(−2)3 = (−2) × (−2) × (−2) = −8
That is −8.
= −8 − 2(−2)
3 Times and divide
Times comes before minus.
2(−2) = 2 × (−2)
+ × − = −
2(−2) means 2 times −2.
Plus times minus is minus.
2 times 2 is 4.
So we get −4.
= −8 − (−4)
4 Plus and minus
Taking away a negative is the same as adding.
− (−) = +
So −8 − (−4) becomes −8 + 4.
= −8 + 4
Start at −8.
Go up 4.
We land on −4.
f(−2) = −4
So f(−2) = −4.
Let's look back.
First: put the number in.
Then: powers.
Then: times and divide.
Last: plus and minus.
▶ Watch it solved
