Question

Create the equation of the transformation of f(x)=∣x∣ given the following: reflected, shifted up 3 units, shifted right 4 units, stretched by a factor of 2.

Answer 1

To transform the function f(x) = |x| by reflection, shifting up 3 units, shifting right 4 units, and stretching by a factor of 2, follow these steps to get the result as f(x) = -2|x - 4| + 3.

Step-by-step explanation:

The transformation of the function f(x) = |x| can be achieved by following these steps:

1. Reflection: Multiply the function by -1 to reflect it over the x-axis. The equation becomes f(x) = -|x|.
2. Shift up 3 units: Add 3 to the function to shift it upwards. The equation becomes f(x) = -|x| + 3.
3. Shift right 4 units: Substitute (x - 4) for x in the equation to shift it 4 units to the right. The equation becomes f(x) = -|x - 4| + 3.
4. Stretch by a factor of 2: Multiply the function by 2 to stretch it vertically. The equation becomes f(x) = -2|x - 4| + 3.