Step by step
The question
Question: find h(3) for h(x) = −x² + 1.
h(x) = −x2 + 1
h(x) is read "h of x".
It is a rule, called a function.
A number goes in for x.
The rule gives one answer out.
h(x) = "h of x"
x goes in → an answer comes out
1 Put the number in
h(3) means: put 3 in place of every x.
Every x becomes 3.
h(3) = −32 + 1
2 Powers
Powers come before plus.
In −3², the power is only on the 3.
The minus stays in front.
Order: ( ) → x² √ → × ÷ → + −
Careful!
It is not (−3)².
Without brackets, the minus stays outside.
Careful: not −32 = 9 ✗
3² means 3 times 3.
32 = 3 × 3 = 9
That is 9.
= −9 + 1
3 Plus and minus
Start at −9.
Go up 1.
We land on −8.
h(3) = −8
So h(3) = −8.
Let's look back.
First: put the number in.
Then: powers.
Last: plus and minus.
Answer
h(3) = −8