Friday

November 28, 2014

November 28, 2014

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

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 12:37pmI 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 12:38pm8th line should have said

-3 = a

(but you probably guessed that was a typo)

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

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

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

**Answer this Question**

**Related Questions**

precalculus - How do I find the vertical/horizontal compression/stretch? For the...

algebra 2 - What are two different transformations that will transform f(x)=5x+3...

Pre-Calculus - Need help with this question, dont get it. Given the relation x^2...

Pre-Calculus Graphs expansions/compressions - Need help with this question, dont...

math - the range for the graph of f(x)=-2(x-3)^2+7 is only affected by: a) the ...

math - The sinusoid y=3cos(x+3)-2 has which of the following? a. phase shift of ...

Precalculus - Whats the value of a? =-= For the graph, determine the equation of...

Math - So I have a question regarding advanced functions, logarithm stuff. here ...

math - what is the equation that responds to a vertical shift up 3 and a ...

Algebra 1 - Describe the effect of the transformation. (x,y)--->(x,-7y) A. ...