Transformations

[sleek sorrel]

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[vital sable]

I attempted to solve this on my own, but found that it was difficult to retrieve the factors in which the graph was stretched/compressed in

I was able to figure out that it is shifted 4 units left and 2 units down

but that's about as far as I got

I know the points have significance but say I did plug in the points/vertical and horizontal translations

in the formula f(x)=af(k(x-d))+c I would still be missing either a or k which means it wouldn't be solvable algebraically

[cobalt pollen]

quickly gonna clarify ive never learned translating cubics

so does a(x-h)^3-k work or not

like a cubic is just a parabola but slightly steeper and one side is flipped

[vital sable]

I don't think there's necessaraly a specific formula for cubics, it would probably be just the formula stated above with a cube as the exponent for (x-d)

[cobalt pollen]

why is it af

[vital sable]

the f doesn't really have any significance, it's more of a filler in the formula

I assume it means a at y

but I've never personally touched it

[cobalt pollen]

try a(x-h)^3-k ?

f(k(x-d) is just fk(x-d)

and you can just make fk one variable i suppose

[vital sable]

yikes, I get 3=-731a

[vital sable]

for this

[cobalt pollen]

wait i just re-read the question they want you to say horizontal and vertical shifts as a number independently dont they