What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing and is represented as being shifted 6 units to the right as compare to the function .

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)

                     horizontal shift: c units to right

So

Considering the function

The graph is shown below. The first figure is representing .

Now, considering the function

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 is shown below in second figure. It is clear that the graph of    is shifted 6 units to the right as compare to the function .

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing and is represented as being shifted 6 units to the right as compare to the function .