Question

Given the function f(x)=x^3+x^2-2x+1, what is the resulting function when f(x) is shifted to the left one unit

Answer 1

simply replace each occurrence of `x` by `x+1`

Answer 2

Still trying to find a way to explain as simply as possible WHY that action would do the desired shift.. :D

oh well ,never mind

Answer 3

So f(x+1)=(x+1)^3+(x+1)^2-2(x+1)+1?

Answer 4

bit tricky to explain - may be we need to go back in time and see how to fix the origin

Answer 5

As I said.. never mind. ^^

Answer 6

Excellent ! @Majestic4321 thats right !!

Answer 7

So then it would reduce to f(x-1)=x^3-2x^2-x+3?

Answer 8

\[f(x)=(x+1)^{3}+ (x+1)^{2}-2(x+1)+1\]

Answer 9

Right but that's not a choice so it would have to reduce right?

Answer 10

Is this the choice

Answer 11

feed it to wolfram :
http://www.wolframalpha.com/input/?i=simplify+%28x%2B1%29%5E3%2B%28x%2B1%29%5E2-2%28x%2B1%29%2B1

Answer 12

No.name yes it is

Answer 13

then that is indeed the choice ,

Answer 14

Thank you:) I second guess myself a lot

Answer 15

no problem

Answer 16

hey no, wait a sec

Answer 17

What

Answer 18

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

This is shift right transformation - Not the one the question was asking you to find

Answer 19

For left shift, ou need to find : f(x\(\color{Red}{+}\)1)

Answer 20

Oh... SO than it would be f(x+1)=x^3+4x^2+3x+1?

Answer 21

I think all of the choices are wrong...

\(f(x + 1) = x^3 + 4x^2 + 3x + 1\) and \(f(x) = x^3 + x^2 - 2x + 1\) represent the same function. :P

Answer 22

yes they refer to the function f itself !

f(x+1)=x^3+4x^2+3x+1 is \(\large \color{red}{\checkmark}\) @Majestic4321

Answer 23

My options with positive one are f(x)+1=x^3+x^2-2x+2 or f(x+1)=x^3+4x^2+3x+1

Answer 24

Okay thanks haha

Answer 25

np, you seem new here... let me take a moment to welcome you :)

\(\large \color{green}{\text{Welcome to Openstudy !}}\)

Answer 26

Yes I am thank you:)