Question

Use any graphing utility to graph f(x)=x^2 and g(x)=(x-4)^2 on the same plot. How is the graph of g(x) related to the graph of f(x)? Explain the relation between the graphs.

Answer 1

Given the functions:

$\begin{gathered} f(x)=x^2 \\ g(x)=(x-4)^2 \end{gathered}$

The graph of the functions will be as follows:

As shown:

The blue graph represents the function f(x).

The red graph represents the function g(x).

F(x) is the parent function of the function g(x).

Translation of the function f(x) 4 units right will give the function g(x).