Question

Given the function f(x) = x3 + x2 - 2x + 1, what is resulting function when f(x) is shifted to the left 1 unit?

Answer 1

To shift \(f(x)\) \(b\) units to the left, evaluate \(f(x + b)\).

Answer 2

In this case, \(b = 1\), so evaluate \(f(x + 1)\).

Answer 3

Can you show me how to do that? I am very confused.

Answer 4

@Hero

Answer 5

\(f(x + 1) = (x + 1)^3 + (x + 1)^2 - 2(x + 1) + 1\)

Answer 6

Expand the right side

Answer 7

Ohh okay i see. Would I combine like terms now?

Answer 8

There are no like terms to combine at the moment. You can't combine exponents like that. You have to expand each term first.

Answer 9

Do I need to find the GCF? @hero

Answer 10

Hang on a minute...

Answer 11

So you could start by factoring out \(x + 1\) to get
\((x + 1)((x + 1)^2 + (x + 1) - 2) + 1\)

That would help make simplifying this much easier.

Answer 12

And then what should I do after that?

Answer 13

Expand \((x + 1)^2\)

Answer 14

(x+1)(x+1) right?

Answer 15

Correct
\((x + 1)^2 = (x + 1)(x + 1)\)

Answer 16

Alright, now what do I do?

Answer 17

Multiply\( (x+1)(x+1)\) completely to quadratic form.

Answer 18

x=-1

Answer 19

\(\begin{align*}(x + 1)(x + 1) &= x(x + 1) + 1(x + 1) \\&= x^2 + x + x + 1 \\&=x^2 + 2x + 1\end{align*}\)

Answer 20

Ohhh okay I understand now. I think I've got the answer to the whole problem, can you check it?

Answer 21

Let's see what you have.

Answer 22

f(x + 1) = x3 + 4x2 + 3x + 1

Answer 23

Correct, but just remember to use a caret for exponents.

Answer 24

Great job.

Answer 25

Okay thank you!!

Answer 26

Can you please show the work you did to arrive at that result?