8. Define a function that transforms the parent root function with a horizontal compression by a factor of 2 and a downward shift of 6 units.
A. f(x)= n/2(x-3)
B. f(x) = 2n/x-6
C. f(x)=2n/x-6
D. f(x)=n/2x-6
D. f(x)=n/2x-6
To define a function that represents a parent root function with a horizontal compression by a factor of 2 and a downward shift of 6 units, we'll need to modify the standard root function f(x) = √x.
Let's break down the steps:
1. Horizontal Compression: To horizontally compress the function by a factor of 2, we need to multiply the input (x) of the function by 2. This will make the function stretch horizontally, effectively compressing the graph. The transformation will look like: f(x) = √(2x).
2. Downward Shift: To shift the function downward by 6 units, we need to subtract 6 from the function. This will cause the graph to move downward while keeping the same shape. The transformation will look like: f(x) = √(2x) - 6.
Therefore, the correct answer is option C: f(x) = √(2x) - 6.
The correct answer is:
D. f(x) = (n/2)x - 6
To apply a horizontal compression by a factor of 2, we multiply the x inside the parentheses by 2. This means that the coefficient of x is now n/2.
To apply a downward shift of 6 units, we subtract 6 from the parent function. This is represented by -6 at the end of the equation.
So, the correct function would be f(x) = (n/2)x - 6.