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 1 unit?

Answer 1

when you shift a function b (number of) units to the left,
you are essentially taking f(x+b).

Answer 2

I have no idea man.

Answer 3

so for b units to the left you would be getting:
g(x)=(x+b)^3+(x+b)^2-2(x+b)+1

Answer 4

now, your b, that you are shifting to the left by, is 1.

Answer 5

Hmm.... How did you do that? lol Explain?

Answer 6

sure, want to know why adding (x\(\normalsize\color{slate}{ \tt +b }\)) means a shift to the left, or just want to see what I did in this situation?

Answer 7

why when you add (x+b) it shifts to the left? Is it because its positive?

Answer 8

was thinking about where to start.
lets do this.

if you shift a line you shift it up and left, right?

Answer 9

so see as you shifted the line up by "a" units, you have also shifted it to the left....
that is 1 reason.

because by a line, when you add y=(x+a) inside the parenthesis, and add y=(x)+a outside the parenthesis, you are getting that same function, y=x+5.

even though (x+a) is a shift to the left, and (x)+a is a shift up (by a units, in both).

Answer 10

this is a one reason....

Answer 11

OHHHHH!! Ok, I see what you mean! They explained this in my lesson but didn't focus on it to much. Thanks man!

Answer 12

same way, you will see that when you shift the line down, you are also shifting it to the right...