The transformed polynomial function is G(x) = 27x^3 + 4x^2 - 186x + 144.
Given:
F(x) = 9x^3 + x^2 - 62x + 48
x + 3
We need to find the transformed polynomial function.
The transformation consists of two parts: a vertical shift and a horizontal shift. The vertical shift is determined by the term "x + 3", and the horizontal shift is determined by the coefficient of x^2 in the original polynomial function.
Vertical shift: The vertical shift is 3 units up because the term "x + 3" is added to the original function. The new vertical shift is 3 units up.
Horizontal shift: The horizontal shift is determined by the coefficient of x^2 in the transformed function. In the original function F(x), the coefficient of x^2 is 1, and in the transformed function, the coefficient of x^2 is 1 + 3 = 4. The new horizontal shift is 3 units to the right.
To find the new coefficients, we multiply the original coefficients by the vertical shift and add the horizontal shift:
Coefficient of x^3: 9 * 3 = 27
Coefficient of x^2: 1 * (1 + 3) = 4
Coefficient of x^1: -62 * 3 = -186
Constant term: 48 * 3 = 144
Now, we write the transformed polynomial function:
G(x) = 27x^3 + 4x^2 - 186x + 144
So, the transformed polynomial function is G(x) = 27x^3 + 4x^2 - 186x + 144.
Complete question:
Solve f(x) = 9x^3 + x^2 - 62x + 48; x + 3