g(x) = abs(f(x))
[abs = absolute value]
How exactly do I explain this transformation? I don't think "y-values turn positive, matching x-values of f" works very well.
An example of another transformation:
g(x) = 3f(x)
~Vertical dilation by a factor of 3.
So how do I describe the absolute value transformation?
thanks!
I'd go for "negative y-values are reflected in the x-axis", but my terminology may be out of date.
Try
"reflection about the x-axis ∀ f(x)<0"
To accurately describe the transformation when we have g(x) = abs(f(x)), you can use the following explanation:
When a function is modified by an absolute value, the resulting graph tends to spread away from the x-axis. This occurs because the absolute value function takes any negative y-values and makes them positive. As a result, the graph of g(x) = abs(f(x)) will only have non-negative y-values, mirroring the x-values of the original function f(x).
To explain this transformation more precisely, you can use the following steps:
1. Begin with the graph of the original function f(x).
2. Identify any portions of the original graph where the y-values are negative.
3. When taking the absolute value of the function, those portions of the graph will be reflected across the x-axis, resulting in positive y-values.
4. The new graph, g(x), will essentially consist of the original graph of f(x), but with the negative parts "flipped" to their positive counterparts.
It is useful to note that this transformation does not affect any portions of the graph where the y-values are already positive.
By following these steps and explaining the behavior of the absolute value function, you can accurately describe the transformation when g(x) = abs(f(x)).