Precalculus

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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 -

    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 -

    8th line should have said
    -3 = a

    (but you probably guessed that was a typo)

  • Precalculus -

    So it is a vertical stretch by -3?

  • Precalculus -

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

  • Precalculus -

    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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