Determine the equation of the function that has the indicated transformation applied to it.
f(x)= 3(x+1)^2-2
Is it 6(x+1)^2-2?
or 9(x+1)^2-2?
To determine the equation of the function that has the indicated transformation applied to it, we start with the original function f(x) = 3(x+1)^2 - 2.
The transformation in this case is multiplying the whole function by a constant. To find the new equation after the transformation, you need to apply the constant multiplication to every term in the original equation.
In this case, the original equation is f(x) = 3(x+1)^2 - 2.
Multiplying the entire equation by 2 gives us:
2 * f(x) = 2 * [3(x+1)^2 - 2]
Distributing the multiplication:
2 * f(x) = 2 * 3(x+1)^2 - 2 * 2
Simplifying the equation:
2 * f(x) = 6(x+1)^2 - 4
So, the correct equation after multiplying the function by 2 is:
2 * f(x) = 6(x+1)^2 - 4
Therefore, the answer is not 6(x+1)^2 - 2 or 9(x+1)^2 - 2. It is 6(x+1)^2 - 4.