The function f is defined by f(x) = 3x^2 - 2x + 4. What is the value… Step by Step

Step by step

The question

Question: find f(−1) for f(x) = 3x² − 2x + 4.

f(x) = 3x² − 2x + 4

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

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Put the number in

f(−1) means: put −1 in place of every x.

We write it in brackets.

The brackets keep the minus with the number.

f(−1) = 3(−1)² − 2(−1) + 4

2 Powers

Everyone uses the same order, so we all get the same answer.

Powers come first.

Order: Powers → × ÷ → + −

(−1)² means −1 times −1.

Minus times minus is plus.

(−1)² = (−1) × (−1)

= 1

− × − = +

That is 1.

= 3(1) − 2(−1) + 4

3 Times and divide

Times comes before minus and plus.

3(1) means 3 times 1.

3(1) = 3 × 1

3 times 1 is 3.

= 3 − 2(−1) + 4

Times comes before minus and plus.

2(−1) means 2 times −1.

2 has no sign, so it is plus.

Plus times minus is minus.

2(−1) = 2 × (−1)

+ × − = −

2 times 1 is 2.

So we get −2.

= 3 − (−2) + 4

4 Plus and minus

Plus and minus: we go from left to right.

Taking away a negative is the same as adding.

Plus and minus: left → right

− (−) = +

So 3 − (−2) becomes 3 + 2.

= 3 + 2 + 4

3 plus 2 is 5.

= 5 + 4

5 plus 4 is 9.

f(−1) = 9

So f(−1) = 9.

5 Pick the choice

Our answer is f(−1) = 9.

That is choice C.

C) 9

6 Why not the others

A is 3.

Wrong: (−1)² is 1, not −1.

A) 3 ✗ (−1)² is 1, not −1

B is 5.

Wrong: −2 × (−1) is +2, not −2.

B) 5 ✗ −2 × (−1) is +2, not −2

D is 15.

Wrong: squared 3 × (−1): only the x is squared.

D) 15 ✗ squared 3 × (−1): only the x is squared

Let's look back.

First: put the number in.

Then: powers.

Then: times and divide.

Then: plus and minus.

Then: pick the choice.

Last: why not the others.

Answer