Question

Using function notation, describe the transformation. x^2+y^2=1 --> (x-7)^2 + (y+4)^2 = 1

PLEASE HELPPPPP!!!

Answer 1

f(x - 7) - 4

Translation: < 7 , -4 >

Explanation:

x^2+y^2=1

Centre: (0,0)

(x-7)^2 + (y+4)^2 = 1

Centre: (7,-4)

Translation: < 7 , -4 >

If the first function is f(x), the transformed function is:

f(x - 7) - 4

Answer 2

f(x - 7) - 4 (if f(x) is the original function)

Explanation:

The equation of a circle is:
`(x-h)^2+(y-k)^2=r^2`, where (h, k) is the centre and r is the radius.

The original function is a circle with centre at (0, 0) and radius 1. The new function is a circle with centre at (7, -4) and radius 1. So it's simply a translation of the first one.

In fact, it's just a translation 7 units right and 4 units down. So the function notation is f(x - 7) - 4, where f(x) is the original function.