Answer:
The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing [tex]f(x) = x^2[/tex] and [tex]\:f\left(x\right)=\left(x-6\right)^2[/tex] is represented as being shifted 6 units to the right as compare to the function [tex]f(x) = x^2[/tex].
Step-by-step explanation:
When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.
For example:
Type of change Effect on y = f(x)
[tex]y = f(x - c)[/tex] horizontal shift: c units to right
So
Considering the function
[tex]f(x) = x^2[/tex]
The graph is shown below. The first figure is representing [tex]f(x) = x^2[/tex].
Now, considering the function
[tex]\:f\left(x\right)=\left(x-6\right)^2[/tex]
According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.
The graph of [tex]\:f\left(x-6\right)=\left(x-6\right)^2[/tex] is shown below in second figure. It is clear that the graph of [tex]\:f\left(x-6\right)=\left(x-6\right)^2[/tex] is shifted 6 units to the right as compare to the function [tex]f(x) = x^2[/tex].
The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing [tex]f(x) = x^2[/tex] and [tex]\:f\left(x\right)=\left(x-6\right)^2[/tex] is represented as being shifted 6 units to the right as compare to the function [tex]f(x) = x^2[/tex].
