Question

Given \[f( - 3x)\],how do you describe the transformation?

Answer 1

Hint: The above question is based on function transformation. In function transformation, the original function f(x) represented on the cartesian plane should be transformed to \[f( - 3x)\]by reflecting and compressing the curve according to the coefficients and sign of the function.

Complete step by step answer:
A function transformation follows a sequence of transformations. By applying a transformation to these graphs, we will obtain new graphs that still have properties of the old one.
In the above question where the function is given as \[f( - 3x)\] where this function will transform in the graph by reflection and scaling.
Since, the original function is \[f(x)\] and the transformed function is \[f( - 3x)\]
The difference between the two is -3.
Further when the reflection transformation is applied because of the negative sign. This sign indicates it is reflected in the y-axis.
Since the coefficient 3 is multiplied rather than in addition with \[x\], it is a scaling instead of a shifting. A scale will multiply/divide coordinates and this will change the appearance as well as the location.
The 3 is grouped with the x, so it is a horizontal scaling or horizontal compression. A horizontal scaling multiplies/divides every x-coordinate by a constant while leaving the they-coordinate unchanged.
 \[( - 3)\] tell us the horizontal compression of \[\dfrac{{ - 1}}{3}\]
It can be written in the format \[x' = \dfrac{x}{b}\]where b is the coefficient with \[x\] within the brackets and \[x'\]is the function of \[x\].

Note:
An important thing to note is that the function can be reflected about an axis by multiplying by a negative sign. For example, to reflect on the y-axis, multiply every x by -1 to get -x. To reflect about the x-axis, multiply f(x) by -1 to get -f(x).