Can someone help me with this question? I got the transformation for horizontal shift and vertical shift, however, I don't know how to find the vertical/horizontal compression/stretch.

Question

1. Describe the transformations that were applied to the parent function to create the graph shown below. Then write the equation of the transformed function.

Parent function y=x^4

Here is the link to graph:

imgur dot com/Gkaln

Answer 1

I looked your graph and the new vertex is (-1,4)

so y = x^4 must have been translated to
y = (x+1)^4 + 4
but there could also be a compression , so let the new curve be

y = a(x+1)^4 + 4
from the graph we can see that (0,1) lies on the new curve
1 = a(1^4) + 4
-3 - a

so we have y = -3(x+1)^4 + 4
test for the other point shown
let x = -2
y = -3(-1)^4 + 4
= 1

all looks good

Answer 2

8th line should have said
-3 = a

(but you probably guessed that was a typo)

Answer 3

So it is a vertical stretch by -3?

Answer 4

How did you find out what a is if you knew it was UP 4, left 1?

Answer 5

Yes, the maginitude of the stretch is 3,
the - tells me the curve is opening downwards

I knew since the vertex was (-1,4)
and the parent graph of y = x^4 has a vertex at (0,0)
the graph must have moved 1 unit to the left and 4 units up

so we would get
y-4 = (x+1)^4
moving the -4 to the right made it +4

but y = (x+1)^4 + 4
would not pass through (0,1) as your picture shows.
so there must have been a stretch/compression.
that would be caused by some number in front of
(x+1)^4
so that is why I chose y = a(x+1)^4 + 4
subbing in the point (0,1) gave me a value of
a = -3