Answer:
reflection over the x-axis
Explanation:
You want a description of the transformation that gets you from f(x) to g(x) = a·f(x), for the values shown in the table.
Transformations
We are generally concerned with four (4) kinds of transformations. Each makes a recognizable modification to a function f(x).
- Horizontal translation right 'h' units: f(x) ⇒ f(x -h)
- Vertical translation up 'k' units: f(x) ⇒ f(x) +k
- Horizontal compression by a factor of k: f(x) = f(kx)
- Vertical expansion by a factor of k: f(x) = k·f(x)
Reflection
Reflection across the x-axis will occur when the vertical expansion factor is negative.
Reflection across the y-axis will occur when the horizontal compression factor is negative.
Application
Here, you're given the relation ...
g(x) = a·f(x)
Using the first column of the table, you can fill in this equation as ...
g( -1) = a·f(-1)
-4 = a·(4)
Dividing by 4 gives the value of 'a':
a = -1
This vertical scale factor has a magnitude of 1 and a negative sign. This means the graph is not vertically scaled, but is reflected across the x-axis.
The transformation applied to f(x) is reflection across the x-axis.