Transformation f ty transform graph y=x^2 or y=|x| graph for f by hand
f(x)=2|x-6|-4
To transform the graphs of y = x^2 and y = |x| to the graph of f(x) = 2|x-6| - 4 by hand, you would need to follow a few steps:
Step 1: Shift the graph horizontally:
In order to shift the graphs of y = x^2 and y = |x| horizontally by 6 units to the right, you need to replace x with x - 6. This will shift the entire graph horizontally to the right by 6 units.
So, the new equation becomes:
y = |x - 6|^2 (for y = x^2)
y = |x - 6| (for y = |x|)
Step 2: Scale the graph vertically:
To scale the graphs vertically by a factor of 2, you need to multiply the y-coordinate by 2. This will stretch the graph vertically.
For y = |x - 6|^2, the equation becomes:
y = 2|x - 6|^2
For y = |x - 6|, the equation becomes:
y = 2|x - 6|
Step 3: Shift the graph vertically:
To shift the graphs downwards by 4 units, you need to subtract 4 from the entire equation. This will move the graph downward.
For y = 2|x - 6|^2, the equation becomes:
y = 2|x - 6|^2 - 4
For y = 2|x - 6|, the equation becomes:
y = 2|x - 6| - 4
Now, you have transformed the graphs y = x^2 and y = |x| into the equation f(x) = 2|x-6| - 4.