Transformations

[sick cloud]

Can someone let me know if I’m anywhere near the right answer?

[cerulean flame]

Can you please show the full problem?

I can't figure out what you're trying to solve otherwise

[flint zealot]

alr so doing it with a table is a bit… 😬

it becomes tedious

and also a bit unnecessary :p

@sick cloud this is alg 2 right

now while mathematicians will say memorizing formulae is bad advice, i find it hard to describe this question easily and intuitively

as of now, use this:

$$
Vf\left(\frac{x-u}{U}\right)+v
$$

[orchid torrent]

tota nox

[flint zealot]

essentially, rewrite the equation so that it looks like this.

once you have done this, horizontally stretch/squish the graph by a factor of U and vertical stretch/squish it by V.

then, move the graph horizontally by u and vertically by v

so your equation would become

$$
\textcolor{gray}{1}f\left(\frac{x-(-4)}{-1/2}\right)-5
$$

[orchid torrent]

tota nox

[flint zealot]

so you redraw the graph scaled horizontally by -1/2 (reflect it and squish it to half of what it is); moved 4 left; and moved 5 down.

alternatively, you could use this which does the same thing:

$$
\frac{y-v}{V}=f\left(\frac{x-u}{U}\right)
$$

[orchid torrent]

tota nox

[flint zealot]

so we would get

$$
\frac{y-(-5)}{1}=f\left(\frac{x-(-4)}{-1/2}\right)
$$

[orchid torrent]

tota nox

[lapis belfry]

not pretty sure about your approach, but you should consider beginning with the following hints
$$f(x+2) = (x+2)^2$$
$$f(2x) = (2x)^2$$
$$f(2x+2) = f(2(x+1)) = [2(x+1)]^2$$

[orchid torrent]

This is sad 😢

[flint zealot]

@sick cloud

i made a cheat sheet for how to do any of these types of questions

of you have any questions lmk

[wild hearth]

Oooo this is extremely helpful

Can I keep this?