Answer:
Horizontal translation in the [tex]+x[/tex] direction.
Step-by-step explanation:
A function of the form [tex]f(x)[/tex] experiments an horizontal translation when the following substitution is applied:
[tex]x \to x + a[/tex], where [tex]a \in \mathbb{R}[/tex]
If [tex]a > 0[/tex], the function is translated in the [tex]-x[/tex] direction, whereas [tex]a < 0[/tex] is the case for the function being translated in the [tex]+x[/tex] direction.
The effect on the graph can be defined by a composition between two function:
[tex]f(x) = x^{2}[/tex], [tex]g (x) = x-6[/tex]
[tex]f\,\circ\,g\,(x) = (x-6)^{2}[/tex]
The resulting expression represents a horizontal translation in the [tex]+x[/tex] direction.
Finally, we plot [tex]f(x)[/tex] (red) and [tex]f\,\circ g\,(x)[/tex] (blue) by a graphing tool and proved the certainty of this theory.
