The general equation of a circle is given by:
(x-a)^2+(x-b)^2=r^2
where:
(a,b) is the center
r is the radius
given the equation:
x^2+y^2=36
it means that the equation is centered at (0,0) with radius of 6 units. Thus a translation of 5 units to the left and 4 units up, will change the new center to
(-5,4)
thus the equation will be:
(x+5)^2+(y-4)^2=36
Answer: (x+5)^2+(y-4)^2=36
Answer:
A reflection in the x-axis, and a vertical translation of 8 units down
Step-by-step explanation:
The given function is
![f(x) = \sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%5Csqrt%5B3%5D%7Bx%7D%20)
The transformed function is
![g(x) = - \sqrt[3]{x} - 8](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20-%20%20%5Csqrt%5B3%5D%7Bx%7D%20%20-%208)
To see the transformation that occurred, we can rewrite g(x) in terms of f(x).
That is:

Therefore f(x) is reflected in the x-axis and translated 8 units down.
The resulting graph decreases from left to right over its entire domain.
the answer is in the attachment
Hope it helps