Posted by **Melinda** on Saturday, December 10, 2011 at 12:16pm.

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.

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

- Precalculus -
**Reiny**, Saturday, December 10, 2011 at 12:37pm
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

- Precalculus -
**Reiny**, Saturday, December 10, 2011 at 12:38pm
8th line should have said

-3 = a

(but you probably guessed that was a typo)

- Precalculus -
**Melinda**, Saturday, December 10, 2011 at 12:39pm
So it is a vertical stretch by -3?

- Precalculus -
**Melinda**, Saturday, December 10, 2011 at 12:43pm
How did you find out what a is if you knew it was UP 4, left 1?

- Precalculus -
**Reiny**, Saturday, December 10, 2011 at 2:37pm
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

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