Question

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

PLEASE HELP

Answer 1

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

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

Answer 2

5f(x + 1) - 4

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.