Using translation concepts, it is found that the equation that represents the new function is:
The cube root parent function is given by:
![y = \sqrt[3]{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
<h3>Translation:</h3>
The function goes through these following translations:
- Vertically stretched by a factor of 3, that is, it is multiplied by 3, hence
![y = 3\sqrt[3]{x}](https://tex.z-dn.net/?f=y%20%3D%203%5Csqrt%5B3%5D%7Bx%7D)
.
- Reflected over the x-axis, that is, it is multiplied by -1, hence
![y = -3\sqrt[3]{x}](https://tex.z-dn.net/?f=y%20%3D%20-3%5Csqrt%5B3%5D%7Bx%7D)
.
- Translated 8 units down, that is, 8 is subtracted from the function, hence
![y = -3\sqrt[3]{x} - 8](https://tex.z-dn.net/?f=y%20%3D%20-3%5Csqrt%5B3%5D%7Bx%7D%20-%208)
.
Then, the equation is:
To learn more about translation concepts, you can take a look at brainly.com/question/13671886
Answer:
(x - 3)² + (y + 9)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Given area = 25π , that is
πr² = 25π ( divide both sides by π )
r² = 25 ( take the square root of both sides )
r = 
= 5
With centre (h, k) = (3, - 9 ) and r = 5 , then
(x - 3)² + (y - (- 9) )² = 5² , that is
(x - 3)² + (y + 9)² = 25
<span>f(x)= x³-x²-9x+9 has x², so it will be
many to one function ( one value of y will correspond several values of x).
Answer is B.</span>
