Question

Somebody please help, I'm clueless.
Write the equation for a translation to the right 2 units and then down by 1 unit to f(x)=x^3+2x^2+x-3

Answer 1

oops right 2 units, ok us
\[f(x-2)\]

Answer 2

then down one, find \[f(x-2)-1\]

Answer 3

I don't get it?

Answer 4

What satellite73 means is -
new function -
f(x)=[(x-2)^3+2(x-2)^2+(x-2)-3] - 1

Answer 5

So that's the answer?

Answer 6

Yes, although you still have to simplify it.

Answer 7

Well I know how to simplify, but I don't understand how you got the new function.

Answer 8

Let there be a graph y=f(x)

Horizontal transformation ('a' units towards +ive x-axis) -
y=f(x-a)

Vertical transformation ('a' units towards +ive y-axis) -
(y-a)=f(x)
although most people write it as -
y=f(x) + a

There are many more transformations, I can cite some books if you want (completely optional :P )

Answer 9

@TheJonathanP4
So what is it that you still don't understand ?

Answer 10

I'm just not positive what I exactly write down for the answer.
Do I write f(x)=[(x-2)^3+2(x-2)^2+(x-2)-3] - 1

Answer 11

@LastDayWork

Answer 12

You have to simplify the expression in RHS. That will be your final answer.

Answer 13

what is RHS

Answer 14

Shorthand for - Right Hand Side of the equation.

Answer 15

How do I do that? do you mean change it to look like this f(x-2)-1=x^3+2x^2+x-3

Answer 16

@phi Can you please help explain what they're asking me to do.

Answer 17

We can show by pictures.

Answer 18

the three curves are: black (the original curve f(x))
red = the black curve shifted down. we add -1 to f(x)
green = black curve shifted up. we add +3 to f(x)

Answer 19

Does that make sense? to shift a curve up U steps, add +U to the curve. All the y values become U bigger. The x values stay the same.

Answer 20

yes, I understand that

Answer 21

so do *part of the problem*
what is
f(x)=x^3+2x^2+x-3

shifted *down* by one step ?

Answer 22

shifted down means you want f(x) to be smaller by 1 step. In other words you want
f(x) - 1

that means write down f(x)
f(x)=x^3+2x^2+x-3
and add -1 to both sides

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

f(x) - 1 = x^3+2x^2+x-4

Answer 23

okay I see

Answer 24

what do you get if you shift f(x) up by 2 ?

Answer 25

to shift up add outside the function f(x)+b; 'b' being the number of units shifted up. so add 2 to the outside

Answer 26

ok.

now what about shifting sideways ?

Answer 27

to shift left add inside f(x+b) to shift right f(x-b)

Answer 28

so since i have to move to the right 2 units and down 1 unit it would look like
f(x-2)-1=x^3+2x^2+x-3

Answer 29

You also have to replace "x" in the original right hand side with "(x-2)"

Answer 30

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

Answer 31

@phi

Answer 32

yes, but you are missing a -1 at the very end.

you start with
f(x)=x^3+2x^2+x-3

shift down 1:
f(x) - 1 = x^3+2x^2+x-3 - 1
now shift to the right 2 steps:
f(x-2)-1 = (x-2)^3 + 2(x-2)^2 +(x-2) -3 -1

of course you can simplify that.

Here is what both curves look like

Answer 33

it takes a lot of work, but
f(x-2)-1 = (x-2)^3 + 2(x-2)^2 +(x-2) -3 -1
can be re-written as
f(x-2)-1 = x^3-4x^2+5x - 6

Answer 34

what is the identity that will prove 25-4=21