Question

What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(x − 6)?

Answer 1

Answer:

Horizontal translation in the $+x$ direction.

Step-by-step explanation:

A function of the form $f(x)$ experiments an horizontal translation when the following substitution is applied:

$x \to x + a$, where $a \in \mathbb{R}$

If $a > 0$, the function is translated in the $-x$ direction, whereas $a < 0$ is the case for the function being translated in the $+x$ direction.

The effect on the graph can be defined by a composition between two function:

$f(x) = x^{2}$, $g (x) = x-6$

$f\,\circ\,g\,(x) = (x-6)^{2}$

The resulting expression represents a horizontal translation in the $+x$ direction.

Finally, we plot $f(x)$ (red) and $f\,\circ g\,(x)$ (blue) by a graphing tool and proved the certainty of this theory.