Using two function notations, describe the transformation. x^2+y^2=1 –> (x+1)^2 + (y-4)^2 = 25 PLEASE HELP

Question

Using two function notations, describe the transformation. x^2+y^2=1 –> (x+1)^2 + (y-4)^2 = 25
PLEASE HELP

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Skylar 2 weeks 2021-09-27T07:26:27+00:00 2 Answers 0

Answers ( )

    0
    2021-09-27T07:27:49+00:00

    Answer:

    f(x) = 5g(x + 1) + 4

    Step-by-step explanation:

    x^2+y^2=1 –> (x+1)^2 + (y-4)^2 = 25

    Centre: (0,0) –> (-1,4)

    Radius: 1 –> 5

    Let the initial function be g(x) and the transformed function be f(x)

    After stretch

    f(x) = 5g(x)

    After translation:

    f(x) = 5g(x + 1) + 4

    0
    2021-09-27T07:28:14+00:00

    Answer:

    5f(x + 1) – 4

    Step-by-step explanation:

    The equation of a circle is denoted by: (x – h)² + (y – k)² = r², where (h, k) is the centre and r is the radius.

    The original function has a centre of (0, 0) and radius of 1. The new function, though, has a centre of (-1, 4) and a radius of 5. That means that the old function was moved to the left 1 unit, moved up 4 units, and dilated by a factor of 5.

    In function notation, the translations would be f(x + 1) – 4. However, we also need to take into account the dilation. This would be like a vertical stretch, so we have: 5f(x + 1) – 4.

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